Consider a three-category classification problem. Let the prior probabilities: p(Y = 1) = p(Y = 2) = p(Y = 3) = 1/3. The class-conditional densities are multivariate normal densities with parameters: Mi = [0,0], M2 = [1,1]], M3 = (-1,1], = and Σ : 1 0.7 0 0 0.7 ], = Σ2 = 1 0.8 0.2 0.2 0.8 1 Σ3 1 0.8 0.2 0.2 0.8 > Classify the following point x = (0.5, 0.5].
Answers
We classify x as belonging to class 1, since it has the highest posterior probability.
To classify the point x = (0.5, 0.5], we need to calculate the posterior probabilities of each class and choose the class with the highest probability.
The posterior probability of class i given x is given by Bayes' theorem:
P(Y=i|X=x) = P(X=x|Y=i) * P(Y=i) / P(X=x)
where P(X=x|Y=i) is the class-conditional density of class i evaluated at x, P(Y=i) is the prior probability of class i, and P(X=x) is the marginal probability of x (which is the same for all classes in this case).
Using the multivariate normal density formula, we can calculate the class-conditional densities as follows:
f1(x) = (2π|Σ1|)-1/2 exp{-1/2(x-M1)'Σ1^-1(x-M1)} = (2π|Σ1|)-1/2 exp{-1/2(0.5^2+0.5^2)}
f2(x) = (2π|Σ2|)-1/2 exp{-1/2(x-M2)'Σ2^-1(x-M2)} = (2π|Σ2|)-1/2 exp{-1/2[(0.5-1)^2+(0.5-1)^2+2*0.2*(0.5-1)*(0.5-1)]}
f3(x) = (2π|Σ3|)-1/2 exp{-1/2(x-M3)'Σ3^-1(x-M3)} = (2π|Σ3|)-1/2 exp{-1/2[(0.5+1)^2+(0.5-1)^2+2*0.2*(0.5+1)*(0.5-1)]}
Using the given prior probabilities, we have P(Y=1) = P(Y=2) = P(Y=3) = 1/3.
To calculate the b P(X=x), we can use the total probability theorem:
P(X=x) = Σi P(X=x|Y=i) * P(Y=i) = f1(x)*1/3 + f2(x)*1/3 + f3(x)*1/3
Now we can calculate the posterior probabilities:
P(Y=1|X=x) = f1(x)*1/3 / P(X=x)
P(Y=2|X=x) = f2(x)*1/3 / P(X=x)
P(Y=3|X=x) = f3(x)*1/3 / P(X=x)
To classify x, we choose the class with the highest posterior probability:
argmaxi P(Y=i|X=x)
Calculating the posterior probabilities and choosing the maximum, we get:
P(Y=1|X=x) = 0.6356
P(Y=2|X=x) = 0.2113
P(Y=3|X=x) = 0.1531
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Related Questions
The cost of movie tickets at Central Cinema just changed. The old price and the new price are shown for adults and children. How much more does it cost for tickets for 2 adults and 3 children at the new prices then at the old prices?
Answers
Answer:
can u give the prices for the tickets?
An adult ticket costs $2 more than a child ticket
Let x and (x + $2)represent the cost of the child and adult ticket respectively
2(x+ $2) + 3x = $34
now solving for x
2x+ $4 + 3x = $34
5x = $30
x = $6 , the cost of the child ticket.
the cost of adult ticket $6+2=$8
Step-by-step explanation:
The length of a rectangle is 3 cm longer than its width.
If the perimeter of the rectangle is 58 cm, find its length and width.
Answers
The length and width of the given rectangle is 16cm and 13cm.
What is a rectangle?A rectangle is a quadrilateral with four right angles in Euclidean plane geometry. It can also be defined as an equiangular quadrilateral because all of its angles are equal; or a parallelogram with a right angle. A square is a rectangle with four equal-length sides.Formula of perimeter of a rectangle: 2(l+b)
Let, width be 'x' then length will automatically be 'x+3'.
Now, put the values in the formula:
P = 2(l+b)58 = 2(x+3+x)58 = 2(2x + 3)58 = 4x + 64x = 58 - 64x = 52x = 52/4x = 13So, width is 13cm then length is (13+3) that is 16cm.
Therefore, the length and width of the given rectangle is 16cm and 13cm.
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Frances buys an iPhone for $150 and gets a consumer surplus of $200. Her willingness to pay for an iPhone is $ . If she had bought the iPhone on sale for $100, her consumer surplus would have been $ . If the price of the iPhone had been $400, her consumer surplus would have been $
Answers
The concept of consumer surplus refers to the satisfaction that consumers get from purchasing a good or service for a price lower than their maximum willingness to pay. The difference between what they are willing to pay and what they actually pay is the consumer surplus.
Therefore, the consumer surplus that Frances gets for the iPhone she bought for $150 is $200, which means that her willingness to pay for an iPhone is $350. ($150 + $200 = $350)If Frances had bought the iPhone on sale for $100, her consumer surplus would have been $250. ($350 - $100 = $250)If the price of the iPhone had been $400, Frances would not have bought it because her willingness to pay is $350, and the price is more than that.
To summarize, Frances' willingness to pay for an iPhone is $350. If she had bought the iPhone on sale for $100, her consumer surplus would have been $250. If the price of the iPhone had been $400, her consumer surplus would have been zero because she would not have bought the iPhone.
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does anyone know the answer to this question.....0.5x + 1.75 = 10
Answers
Answer:
x = 16.5
Step-by-step explanation:
0.5x + 1.75 = 10
Subtract 1.75 from both sides:
0.5x = 8.25
Divide both sides by 0.5
x = 16.5
Check your work!
0.5(16.5) + 1.75 = 10
8.25 + 1.75 = 10
10 = 10
x = 16.5
By what percent did the price change if the price was $40 and now it is $60?
Answers
Answer:
20 PERCENT
Step-by-step explanation:
BECUASE 40 INTO 60 AND THAT MEAN WE PLUS 20
Answer:
It would go up by 50%
Step-by-step explanation:divide 60 by 40 to get 1.5
then change that to 50% because the extra 1 is the 60 and then change the 0.5 to 50%
What is the height of a right circular cylinder made from a rectangular sheet of lengil
20 cm and breadth 15 cm if it is rolled along its length?
Answers
Answer:
15 cm
Step-by-step explanation:
When the rectangular sheet rolled along its length, the breadth becomes the height of the cylinder, and the length becomes the circle, so the height is 15 cm
How do you graph x= -3
Answers
Answer:
Step-by-step explanation:
Answer:
look at attachment
Step-by-step explanation:
Hope this Helps!! (brainliest please, if possible)
Paige earned $15.50 per hour. She received an 18% raise. If Paige worked 10 hours at her new salary. How much did Paige earn?
Answers
15.50 + 2.79=18.29
Therefore, $18.29 is her hourly pay.
To find how much money she earns in 10 hours, multiply this pay per hour (18.29) times the hours worked (10).
18.29 x 10
182.9
This means that Paige earns $182.90 for working 10 hours.
Hope this helps! Please comment if you need any more explanation and I’ll get back to you ASAP :)
Veuillez m’aider s’il vous plaît à résoudre cette question merci !
2. Un tableur a permis d'estimer l'évolution du taux de la population urbaine en France,
en pourcentage, par :
1(x)=0,00028x^3 -0,0276x^2 +0,968x+62,5
Lorsqu'on modélise
où x est le nombre d'années écoulées depuis 1960.
une évolution par une
Le rythme de croissance (instantané) du taux est assimilé à la dérivée de t. fonction, il faut que ses
a. Calculer la valeur estimée du taux de la population urbaine en 1968. valeurs, son sens de
Calculer le pourcentage d'erreur par rapport à la valeur effective de ce variation et son rythme
taux en 1968, donnée dans le texte.
de croissance soient
b. Exprimer t'(x), puis "(x) en fonction de .x.
compatibles avec les
c. Justifier que la fonction i est croissante sur [0;+ e[ . Interpréter.
données observées.
d. D'après le modèle, au cours de quelle année le rythme de croissance est-il le plus faible?
Est-ce compatible avec les données du texte ?
e. Expliquer pourquoi, à partir d'un moment, la fonction ne peut modéliser l'évolution du
taux de population urbaine.
Answers
Answer:
population and moment ne
Find the limit, if it exists, or show that the limit does not exist. lim(,)→(0,0) 2 2 4
Answers
The limit does not exist.
What is a limit?A limit in mathematics is the value that a function approaches when its input approaches some value. Limits are used to define continuity, derivatives, and integrals in calculus and mathematical analysis.In order for such a limit to occur, the fraction \(\frac{x^{2} }{x^{2} +y^{2} }\) must be comparable to the same value \(L\), regardless of the way we take to get there \((0,0)\).
Try approaching \((0,0)\) along the x-axis.
This means setting \(y=0\) and finding the limit \(lim_{x-0} \frac{x^{2} }{x^{2} +y^{2} }\).
We obtain:
\(lim_{x-0,y=0}\frac{x^{2} }{x^{2} +y^{2} } =lim_{y=0}}\frac{x^{2} }{x^{2} +0 }\\=lim_{x-0}} \frac{x^{2} }{x^{2} } \\\\=lim_{x-0}}1\\=1\)
Now evaluate approaching \((0,0)\) along the y-axis.
This means setting \(x=0\) and finding the limit \(lim_{y-0} \frac{x^{2} }{x^{2} +y^{2} }\).
\(lim_{y-0,x-0} \frac{x^{2} }{x^{2} +y^{2} } =lim_{y-0} \frac{0}{0+y^{2} } \\=lim_{y-0} \frac{0}{y^{2} } \\=lim_{y-0} 0\\=0\)
Approaching the origin via these two methods results in distinct limits.
\(lim_{x-0,y-0} \frac{x^{2} }{x^{2} +y^{2} }\) ≠ \(lim_{y-0,x-0}\frac{x^{2} }{x^{2} +y^{2} }\)
Therefore the limit does not exist.
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The correct question is given below:
Find the limit, if it exists, or show that the limit does not exist.
\(lim_{(x,y) -(0,0)} \frac{x^{2} }{x^{2} +y^{2} }\)
suppose you pick a point uniformly at random from the interval [0, 1]. given your point, your friend picks a point uniformly at random between 0 and your point. (a) find the joint probability distribution of the two points. (b) find the expectation of the product of the two points. (c) find the marginal distribution of the point your friend picks. (d) check that the pdf from (c) satisfies all conditions for being a pdf. (e) find the conditional distribution of your point given your friend point.
Answers
(a) The joint probability distribution of the two points will be 1/x, 0<x<1, 0<y<1
(b) The expectation of the product of the two points will be 1/6
(c) The marginal distribution of the point your friend picks will be (-1/2) lny^2
We have, X=(0,1)
Y | X=X=(0, X)
a) Let f(x,y) be the joint probability distribution of the two points will be:
f(X)=1
f(Y|X)=1/x
\($$\begin{aligned}& f(x, y)=f(X) f(Y \mid X=x)=1 / x, 0 < x < 1,0 < y < x\end{aligned}$$\)
b) Let E(XY) be the expectation of the product of the two points.
\($$\begin{aligned}E(XY)=& \int_0^1 \int_0^x \frac{x y}{x} d y d x=\frac{1}{6} \quad \text { (Decimal : } 0.16667 \ldots \text { ) }\end{aligned}$$\)
c) Let f(y) be the marginal distribution of the point your friend picks.
So, the value of f(y) will be:
\($$\begin{aligned}& \mathrm{f}(\mathrm{y})= \\& \int_y^1 \frac{1}{x} d x=-\frac{1}{2} \ln \left(y^2\right)\end{aligned}$$\)
d)for 0<y<1
\($$\begin{aligned}& f(y) > =0 \\& \int_0^1-\frac{1}{2} \ln \left(y^2\right) d y=1\end{aligned}$$\)
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Find all 3 solutions: 3 − 42 − 4 + 5 = 0
Answers
Answer:
Step-by-step explanation:
If you mean 3x^3 - 42x^2 - 4x + 5 = 0 you can graph it manually or with technology
The roots are 14.09, 0.30 and -0.39 to nearest hundredth.
PLEASE HELP ME!
How much tax is owed or how much refund is expected? Tax due $ 1374 and tax withheld $678.
A. refund $696
B. refund $678
C. tax owed $696
D. tax owed $5678
Answers
Answer:
The answer is C
Step-by-step explanation:
Solve 2x - 3 = 1
Solve for x
Answers
Answer:
x=2
Step-by-step explanation:
Add 3
2x=4
divide by 2
x =2
To solve this you need to get the x by itself. To do this we must move the -3 to the other side of the equation. To do this we add 3 to both sides. Now we have
2x = 4
The next step is to divide both sides by 2 so that the x is alone. 4/2 is 2 so
x=2
Select the correct answer.
This table models function m.
Function n represents a cubic function that passes through the points (-1,0) and (0,2).
Which statement is true?
A.
The y-intercept of m is less than the y-intercept of n.
B.
The y-intercept of m is not given.
C.
The y-intercept of m is equal to the y-intercept of n.
D.
The y-intercept of m is greater than the y-intercept of n.
Answers
Answer:
A.
The y-intercept of m is less than the y-intercept of n.
Step-by-step explanation:
y-intercept of a function:
The y-intercept of a function is the value of y when \(x = 0\)
Function n represents a cubic function that passes through the points (-1,0) and (0,2).
When \(x = 0, y = 2\), and thus, the y-intercept is y = 2.
Function m:
When \(x = 0, y = -6\), and thus, the y-intercept is y = -6, which is a smaller number than 2, so the y-intercept of m is less than the y-intercept of n, and the correct answer is given by option A.
Wich Type of rectangle has not equal side lengths A. Isosceles B. Equilateral C. Scalene D. None of the above
Answers
Answer:
C. Scalene triangle
Step-by-step explanation:
Wich Type of triangle has not equal side lengths A. Isosceles B. Equilateral C. Scalene D. None of the above
scalene triangle can be regarded as triangle whereby all three sides of the triangle have different lengths. the angles in scalene triangle is also
different if measured. Some right triangles can as well be regarded as scalene triangle if other two angles( the legs) are not congruent. It should be noted that Type of triangle which has not equal side lengths is Scalene
When full a 22-gallon gas tank can hold 129.8 pounds of gasoline. Estimate the weight of one gallon of gasoline.
Answers
ANSWER:
\(5.9 \: pounds\)
STEP-BY-STEP EXPLANATION:
Gasoline put into one gallon
\( = \frac{129.8}{22} = \frac{64.9}{11} = 5.9\)
what is the area of the circle us 3.14 to approximate pi pls help
Answers
Answer: 247in
Step-by-step explanation:
Area of a circle is pi radius squared.
So that'll be 3.14 times 9 (because radius is halve if a diameter) squared.
First using Order of Operations squaring the 9, so that'll be 81.
Lastly you multiply π or 3.14.
So 81 x 3.14 is 247. Which is rounded down to the nearest whole number.
Happy Solving.
Create two groups of cards with the SAME SUM using the numbers 8 7 6 2 1 3.
Answers
Some of the groups of cards that have the same sum are:
Group 1 Group 2 Sum
{8, 1} {7, 2} 9
{8, 2} {7, 3} 10
{8, 3} {7, 3, 1} 11
{8, 1, 3} {7, 3, 2} 12
How to determine the groups of cards?From the question, we have the following parameters that can be used in our computation:
Numbers: 8 7 6 2 1 3.
In the above group of numbers, we have
Highest = 8
Least = 1
When these are added, we have
8 + 1 = 9
Another set of numbers that have a sum of 9 is (7, 2)
There are several other numbers that can be created
Some of these numbers are
{8, 2} and {7, 3} with a sum of 10{8, 3} and {7, 3, 1} with a sum of 11{8, 1, 3} and {7, 3, 2} with a sum of 12And several others
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Which expression is the answer
Answers
Answer: option 3
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help please
f − –7/3 = 3
Answers
Answer:
f=2/3
Step-by-step explanation:
Consider the accompanying data on flexural strength (MPa) for concrete beams of a certain type.
5.4 7.2 7.3 6.3 8.1 6.8 7.0 7.6 6.8 6.5 7.0 6.3 7.9 9.0 8.4 8.7 7.8 9.7 7.4 7.7 9.7 8.1 7.7 11.6 11.3 11.8 10.7
The data below give accompanying strength observations for cylinders.
6.2 5.8 7.8 7.1 7.2 9.2 6.6 8.3 7.0 9.0 8.0 8.1 7.4 8.5 8.9 9.8 9.7 14.1 12.6 11.7
Prior to obtaining data, denote the beam strengths by X_{1} ,...,X m and the cylinder strengths by Y_{1} ,...,Y n . Suppose that the X_{j} ^ dagger constitute a random sample from a distrib distribution with mean mu_{2} and standard deviation sigma_{2}
(a) Use rules of expected value to show that overline X - overline Y is an unbiased estimator of mu_{1} - mu_{2}
E( overline X - overline Y )=(E( overline X )-E( overline Y ))^ 2 = mu_{1} - mu_{2} .
E( overline X - overline Y )= E( overline X )-E( overline Y ) nm = mu_{1} - mu_{2}
E( overline X - overline Y )=E( overline X )-E( overline Y )= mu_{1} - mu_{2}
E( overline X - overline Y )= sqrt(E(X) - E(Y)) = mu_{1} - mu_{2}
E( overline X - overline Y )=mm(E( overline X )-E( overline Y ))= mu_{1} - mu_{2} .
Calculate the estimate for the given data. (Round your answer to three decimal places.)
MPa
(b) Use rules of variance to obtain an expression for the variance and standard deviation (standard error) of the estimator in part (a).
V( overline X - overline Y )=V( overline X ) - V ( overline Y ) = sigma_{x} ^ 2 + sigma_{Y} ^ 2
Answers
The standard error of the estimator is 0.478 MPa (rounded to three decimal places).
(a) The mean flexural strength for concrete beams is denoted as μ1. The mean strength of cylinders is denoted as μ2.
Suppose X1, . . ., Xm denote the strengths of concrete beams and Y1, . . ., Yn denote the strengths of cylinders.
(i) Using the expected value properties to show that $\overline{X}-\overline{Y}$ is an unbiased estimator of $μ_{1}-μ_{2}$.
It is well-known that the expected value of a linear combination of random variables is equal to the linear combination of their expected values.
Therefore,$E[\overline{X}-\overline{Y}]=E[\overline{X}]-E[\overline{Y}]=μ_{1}-μ_{2}$
(ii) Calculate the estimate for the given data: Using the formulas for the sample mean and standard deviation for concrete beams and cylinders,$\overline{X}=\frac{1}{m} ∑ X_{i} =7.81$MPa$\overline{Y}=\frac{1}{n} ∑ Y_{i}=8.37$MPa$μ_{1}-μ_{2}=7.81-8.37=-0.56$MPa
(b) Use rules of variance to obtain an expression for the variance and standard deviation (standard error) of the estimator in part (a).Using the formulas for the variance of the sample mean,$Var[\overline{X}]=\frac{\sigma_{X}^{2}}{m} =\frac{0.85^{2}}{26} =0.0282$MPa$Var[\overline{Y}]=\frac{\sigma_{Y}^{2}}{n}=\frac{2.00^{2}}{20} =0.200$MPa$Var[\overline{X}-\overline{Y}]=Var[\overline{X}]+Var[\overline{Y}]=0.0282+0.200=0.2282$MPa.
The standard deviation of the estimator is the square root of the variance:$SE(\overline{X}-\overline{Y})=\sqrt{Var(\overline{X}-\overline{Y})}=\sqrt{0.2282}=0.478$MPa.
Therefore, the standard error of the estimator is 0.478 MPa (rounded to three decimal places).
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2his is a subjective question, hence you have to write your answer in the Text-Field given below. (a) Discuss and explain the properties of indifferent curves. [3] (b) A consumer has a budget of Rs. 200 to be spent on two items, X and Y. Prices of X and Y are Rs. 40 and Rs. 20 , respectively. 1. What is the equation of the budget line? Graphically present it showing the opportunity set of consumption. [2] 2. The marginal utility of X is 50 , while that of Y is 30 . Will the consumer be in equilibrium? What will a rational customer do in this situation? Explain in the light of utility analysis
Answers
Indifferent curves are convex to the origin, and no two can intersect. The slope of the curve is given by the marginal rate of substitution, which shows how much of Y an individual is willing to give up to obtain another unit of X.
The slope of an indifferent curve, therefore, reflects how much an individual is willing to substitute between two goods while still retaining the same level of satisfaction. Indifferent curves are a graphical representation of utility, indicating the amount of satisfaction a consumer obtains from a given combination of two commodities or goods.In contrast, Budget line is a graphical representation of the combination of two goods that a consumer can buy with a given amount of income and prices of goods. The budget line is downward sloping, indicating the number of goods that can be purchased for a given amount of money.The equation of the budget line is given by;
M = PxX + PyY, where M is the total money available for spending, Px is the price of good X, Py is the price of good Y, X is the amount of good X, and Y is the amount of good Y.The equation of the budget line is; 40X + 20Y = 200.On the vertical axis, put Y and on the horizontal axis, put X, the intercepts are X = 5 and Y = 10, the budget line will be at (5,0) and (0,10).The marginal utility of X is greater than the marginal utility of Y. Therefore, the consumer will increase the consumption of X and reduce the consumption of Y until the ratio of marginal utilities of both goods equals the ratio of their prices.The consumer will be in equilibrium when;MUx/Px = MUy/Py.
The indifferent curve and budget line concepts are critical in analyzing consumer behavior and their buying patterns. By understanding the principles of utility analysis, businesses can set prices for their goods and services that ensure consumers are willing to buy them. This, in turn, leads to increased sales, revenue, and profits for the business.
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at a local fitness center, members pay $6 membership fee and $2 for each aerobics class. Nonmembers pay $4 for each aerobics class. For what number of aerobics classes will the cost for members and nonmembers be the same?
Answers
Suppose that the random variables X and Y are independent and you know their distributions.
Which of the following explains why knowing the value of X tells you nothing about the value of Y?
A.
X and Y might be independent.
B.
The mean of X might be different from the mean of Y.
C.
The variance of X might be different from the variance of Y.
D.
All of the above.
Answers
A. X and Y might be independent. Knowing the value of one independent variable tells us nothing about the value of the other independent variable. The mean and variance of X and Y being different does not necessarily mean that knowing the value of one tells us nothing about the other.
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Fully factor
n^2 -4n +3
Answers
Answer:
(n-3) (n-1) :)
Step-by-step explanation:
A delivery truck is transporting boxes of two sizes: large and small. The combined weight of a large box and a small box is 80 pounds. The truck is transporting 60 large boxes and 65 small boxes. If the truck is carrying a total of 4975 pounds in boxes, how much does each type of box weigh? X Large box: pounds Small box: ( pounds 5 ?
Answers
Answer:
small = 35 pounds
large = 45 pounds
Step-by-step explanation:
Let x = large boxes
y = small boxes
two equations can be derived from the question
x + y = 80 equation 1
60x + 65y = 4975 equation 2
multiply equation 1 by 60
60x +60y = 4800 equation 3
subtract equation 2 from 3
5y = 175
y = 35
substitute for y in equation 1
x + 35 = 80
x = 80 - 35
x = 45
Answer and explanation please
Answers
because the cube root of 27 is 3 and 15/3 is 5
In a city, 49% of the adults are male. Of the adults, 24% are male and rent action-movie DVDs and 10% are female and rent action-movie DVDs.
If an adult is randomly picked, the probability that the person rents action-movie DVDs, given that the person is female, is
.
Answers
Answer:
I getting the probability of the adult female that will rent the action movies in DVDs in by dividing the possible probability outcome which is 10% of all adults by the total number of possible outcome. So all of the population of the female is 51% and the ones who rent is only 10%. the probability is 19%
The solution is, 0.20 is the probability that the person rents action-movie DVDs, given that the person is female.
What is probability?Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.
here, we have,
given that,
Data:
A: the adult is a male, P(A) = 0.49
B: the adult rent action-movie DVDs
C: the adult is a female, P(C) = 1 - P(A) = 1 - 0.49 = 0.51
24% of the adults are male and rent action-movie DVDs, then P(A ∩ B) = 0.24
10% of the adults are female and rent action-movie DVDs, then P(C ∩ B) = 0.10
The conditional probability of B (the adult rents action-movie DVDs) given C (the adult is female) is computed as follows:
P(B|C) = P(C ∩ B)/P(C)
= 0.1/0.51
= 0.2
Hence, The solution is, 0.20 is the probability that the person rents action-movie DVDs, given that the person is female.
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An NBA center recently signed a seven-year contract for $121 million. What is the present value of this contract, given a 9% interest rate? In other words, how much must the ball club invest when the contract is signed, so that it can make seven equal payments of $17285714.29, the first one due immediately?
Answers
Answer:
PV= $86,998,184.72
Step-by-step explanation:
Giving the following information:
Annual payments= $17,285,714.29
Number of years= 7
Interest rate= 9%
First, we need to determine the future value incorporating the interest rate.
FV= {A*[(1+i)^n-1]}/i
A= annual payment
FV= {17,285,714.29* [(1.09^7) - 1]} / 0.09
FV= $159,036,085.1
Now, we can calculate the present value:
PV= FV/(1+i)^n
PV= 159,036,085.1/1.09^7
PV= $86,998,184.72