Find the value of a + 2 that ensures the following model is a valid probability model: e α P(x) = 1 + 2/2 X = 0, 1, 2, ... x! Please round your answer to 4 decimal places! Answer:
Answers
The answer is a + 2 = 1 + 2 = 3
The given model is as follows: e α P(x) = 1 + 2/2 X = 0, 1, 2, ... x! Where x! is the factorial of x. We are given that the above model is a valid probability model. This means that the sum of all probabilities must be 1.Let's calculate the probability for each value of x:For x = 0:P(0) = eα(1 + 2/2·0!) = eα(1 + 1) = eα · 2For x = 1:P(1) = eα(1 + 2/2·1!) = eα(1 + 1) = eα · 2For x = 2:P(2) = eα(1 + 2/2·2!) = eα(1 + 1) = eα · 2The sum of probabilities must be equal to 1, so: P(0) + P(1) + P(2) + ... = eα · 2 + eα · 2 + eα · 2 + ...= 2eα(1 + 1 + 1 + ...)The sum of 1 + 1 + 1 + ... is an infinite geometric series with a = 1 and r = 1, which means it has no limit. However, we know that the sum of all probabilities must be 1, so we can say that:2eα(1 + 1 + 1 + ...) = 12eα = 1eα = 1/2Now we can substitute this value of α in any of the equations above to find the value of P(x). For example, for x = 0:P(0) = eα · 2 = (1/2) · 2 = find the value of a + 2 that ensures the model is valid: P(0) + P(1) + P(2) + ... = eα · 2 + eα · 2 + eα · 2 + ...= 2eα(1 + 1 + 1 + ...) = 12eα = 1α = ln(1/2) ≈ -0.6931Therefore, the model is valid when α = ln(1/2).Now, let's find the value of a + 2:P(0) = eα · 2 = e^(ln(1/2)) · 2 = (1/2) · 2 = 1P(1) = eα(1 + 2/2·1!) = e^(ln(1/2)) · (1 + 1) = 1P(2) = eα(1 + 2/2·2!) = e^(ln(1/2)) · (1 + 1) = 1
Know more about probability here:
https://brainly.com/question/31828911
#SPJ11
Related Questions
Mark has 100-foot piece of rope. He cut off a piece that measured 50.3 feet and three pieces that were each 5 feet long. How much rope does mark have left?
Answers
Answer:
34.7 feet
Step-by-step explanation:
50.3 + 5 x 3 = 50.3 + 15 = 65.3
100 - 65.3 = 34.7
Answer:34.7
Step-by-step explanation:
5x3=15
15+50.3=65.3
100-65.3=34.7
mark has 34.7 feet of rope left.
How do the triangle theorems work. Asa aas sas hL?
Answers
Did I do it right? If I didn't, Can u please explain why and give me the correct answer please?
Answers
5/24=0.21
And 6/24 x200=50
I think u right
Answer:
Step-by-step explanation:
1) find the total of candies
3 + 6 + 5 + 2 + 8 = 24
2) divide the number of yellow candies for the total amount of candies
5/24 = 0.21 (correct)
3) use a proportion
6 : 24 = x : 200
x = (200 *6) / 24 = 50 (correct)
claim sizes range between 0 and 1500. the probability that a claim is no greater than 500 is 0.8. claim sizes are uniformly distributed on (0; 500] and on (500; 1500]. calculate the expected claim sizes and its variance.
Answers
The expected claim size is 950 and the variance is 125000/9.
The probability that a claim is no greater than 500 is 0.8, which means the probability of a claim being greater than 500 is 0.2. The claim sizes are uniformly distributed on (0; 500] and on (500; 1500].
Therefore, the probability of a claim being in the range of (0; 500] is 0.8/2 = 0.4 and the probability of a claim being in the range of (500; 1500] is 0.2/2 = 0.1.
The expected claim size is calculated as the weighted average of the claim sizes in each range, where the weight is the probability of a claim being in that range. Thus, the expected claim size is (0.4 x 250 + 0.1 x 1000) = 950.
The variance of the claim size is calculated as the weighted average of the squared deviations from the expected claim size, where the weight is the probability of a claim being in that range. Thus, the variance is (0.4 x (250 - 950)^2 + 0.1 x (1000 - 950)^2) = 125000/9.
Therefore, the expected claim size is 950 and the variance is 125000/9.
For more questions like Probability click the link below:
https://brainly.com/question/30034780
#SPJ4
Latrell wants to paint his bedroom ceiling to look like the sky. He wants it to be 85% blue and 15% white. If he needs 4.25 gallons of blue, how many gallons of white does he need?
Answers
Answer:
0.75 gallons
Step-by-step explanation:
As the statement indicates that Latrell wants the bedroom ceiling to be 85% blue and 15% white and you know that he needs 4.25 gallons of blue which represents the 85%, you can use a rule of three to find the amount that represents the 15% to know the gallons of white that he needs:
4.25 gallons → 85%
x ← 15%
x= (4.25*15)/85
x=0.75
According to this, the answer is that if Latrell needs 4.25 gallons of blue, he needs 0.75 gallons of white.
Simplify the expression (d^7)^6
Answers
Answer:
d^42
Step-by-step explanation:
Hope this helps!
XY and BD are parallel lines. X is a point on AB and C is a point on BD. XB = XC. a) Complete this sentence. Angle XBC = 55° because angles are correspondiner Al 559 Х -Y b) Work out angle BXC. Give a reason for each angle you work out. I B D с
someone help me please I'll give you most brainliest answer
Answers
Answer:
Step-by-step explanation:
∠XBC = 55°
XB = XC. So, ΔXBC is an isosceles triangle
∠XCB = ∠XBC
∠XCB = 55°
In ΔXBC,
∠BXC + ∠XBC + ∠XCB = 180 {Angle sum property of triangle}
∠BXC +55 +55 = 180
∠BXC + 110 = 180
∠BXC = 180 -110
∠BXC = 70°
Answer:
Given : XYAB
Solution:
(a) if XY || AB ad AB is the transversal line
then
<AXY = <XBC (Corresponding angles )
now
(b) since XB = XC XBC is the isosceles triangle
therefore
<XBC = <XCB (angle opposite to equal side are equal)
now , in triangle XBC
<XBC + <XCB + <BXC = 180° (angle sum property)
55 + 55 + <BXC = 180°
<BXC = 180°- 110° <BXC = 70°
hence ,<BXC = 70°
I hope this help u
please help ill give brainilest
Answers
Answer:
y = -2x
Step-by-step explanation:
According to the table, 1 is subtracted from x and 2 is subtracted from y every step.
-2/1x
(rise over run.)
NEED HELP ASAPP DUE SOONNN
Answers
Answer:
\(-9216^{52}\)
Step-by-step explanation:
From the image, each term doubles the base (that is, the -9, -18, -36, etc.)
and increases 5 in the exponent, starting from the 1st term (-9x^2)
Pattern:
-9^2, -9 times 2 = -18, 2 + 5 = 7, -18x^7
Formula (base number):
an = a1 × \(r^{n-1 }\)
a11 = -9 × \(2^{11-1}\)
a11 = -9 × \(2^{10}\)
a11 = -9 × 1024 = -9216
Formula (exponent number):
an = a1 + (n-1)d
a11 = 2 + (11-1)5
a11 = 2 + (10)5
a11 = 2 + 50 = 52
So, the answer is \(-9216^{52}\)
Determine if the given sequence is an arithmetic sequence. If it is, find the common difference, d.
-3, 0, 3, 6, ...
Is this an arithmetic sequence?
O No
O Yes
Answers
We need to solve this question using Arithmetic Progression concept. Yes the given sequence is Arithmetic and value of d is 3.
What do you mean by Arithmetic Progression?A series of numbers called an arithmetic progression or arithmetic sequence (AP) has a constant difference between the terms. One arithmetic progression with a common difference of 2 is the sequence 5, 7, 9, 11, 13, 15,...
The n-th term of the sequence (a n) is provided by: If the first term of an arithmetic progression is a and the common difference between each succeeding component is
{a {n}=a+(n-1)d},
If the AP contains m terms, then a m denotes the final term, which is provided by:
{a {m}=a+(m-1)d}.
The term "finite arithmetic progression" or "arithmetic progression" refers to a finite segment of an arithmetic progression. An arithmetic series is the total of a finite arithmetic progression.
CalculationThe given sequence is -3,0,3,6,....
We know that an=a + (n-1)d where d is the common difference
⇒ 0= -3 + d
∴ d=3
So hence proved that the given sequence is arithmetic.
We need to solve this question using Arithmetic Progression concept. Yes the given sequence is Arithmetic and value of d is 3.
To refer more about Arithmetic Progression , visit:
https://brainly.com/question/6561461
#SPJ1
Find the value of X.
Answers
Answer:-
x=110 degree
Step-by-step explanation:
It's quadrilateral so it's total sum degree is 360
then 40+82+128+x=360
360-(128+82+40)=X
x=360-250
x=110 degree
The solutions to the inequality y ≤ −x + 1 are shaded on the graph. Which point is a solution?
Answers
It should be B children
Bye giggity giggity gamers! nyah :3
Which of the following choices correctly identifies the following Q-Q plots for the normality of residuals assumption? Select one.
Two graphs, A and B, shown side by side. Both graphs share the same axis labels and values. The x-axis is labeled "Theoretical quantiles" and values go from negative three to three. Each tick mark represents one. The y-axis is labeled "Sample quantiles" and values go from negative three to three. Each tick mark represents one. In both graphs, a red line runs from point negative 3 comma 3 up to 3 comma 3. Both graphs contain a series of blue points, but they differ in how well those points approximate the line. In Graph A, the blue dots start around the coordinate negative three comma negative two. The series of blue dots approaches the line around the coordinates negative one comma negative one. The blue dots waver a little above and below the line as the x-value increases. In Graph B, the blue dots are a much closer fit to the red line throughout the graph. They start much closer to the red line and only deviate slightly at the top-right of the graph, around the coordinates two comma two.
1. Both graphs show residuals with a distribution that is not Normal.
2. Graph B shows residuals with a distribution that more closely approximates a Normal distribution than Graph A.
3. Graphs A and B both show residuals with distributions that closely approximate a Normal distribution.
4. Graph A shows residuals with a distribution that more closely approximates a Normal distribution than Graph B.
Answers
The correct identification is that Graph B shows residuals with a distribution that more closely approximates a Normal distribution than Graph A.
Graph B shows residuals with a distribution that more closely approximates a Normal distribution than Graph A.
In the given description, Graph B is described as having blue dots that are a much closer fit to the red line throughout the graph, except for slight deviations at the top-right of the graph. This indicates that the points in Graph B align more closely with the theoretical line, suggesting a closer approximation to a Normal distribution.
On the other hand, Graph A is described as having blue dots that start around the coordinate negative three, negative two, and approach the line around the coordinate negative one, negative one. Additionally, the description mentions that the blue dots waver a little above and below the line as the x-value increases. This implies that the points in Graph A do not align as closely with the theoretical line as in Graph B, indicating a lesser approximation to a Normal distribution.
The correct identification is that Graph B shows residuals with a distribution that more closely approximates a Normal distribution than Graph A.
For more questions on Graph
https://brainly.com/question/19040584
#SPJ8
The average weekly unemployment benefit in Montana is $272. Suppose that the benefits are normally distributed with a standard deviation of $43. A random sample of 8 benefits is chosen in Montana. What is the probability that the mean for this sample is greater than $299?
Answers
From the given question we can extract all the necessary parameters to enable us to find the solution to the question.
We would therefore have the following parameters
\(\begin{gathered} \text{observed }value=X=299 \\ S\tan darddeviation=\sigma=43 \\ \text{sample}=n=8 \\ \text{average}=\mu=272 \end{gathered}\)This would be inserted into the formula given for the z score below
\(z=\frac{x-\mu}{\frac{\sigma}{\sqrt[]{n}}}\)This would then be written as
\(\begin{gathered} z=\frac{299-272}{\frac{43}{\sqrt[]{8}}} \\ z=1.78 \end{gathered}\)We look up the z score on the probability table to get 0.9625. We then subtract from 1 to get the answer
\(p(z>1.78)=0.0375\)ANSWER=0.0375
A café records how people take their coffee. Altogether 71 take milk and 36 take sugar. 21 take both and 24 take neither.
Draw a Venn Diagram showing this information.
How many people were in the survey?
Answers
Lucie is struggling with Geometry and is in need of a private tutor. She has two candidates in mind. The veteran tutor charges $15 for the first session plus $60 per hour afterward. The new college graduate charges $45 for the first session plus $50 per hour afterward. How many hours must these two tutor in order to earn the same amount of money?
Answers
Answer:
2.33 hours
Step-by-step explanation:
Given
Veteran Tutor
\(Charges = \$15\) --- first session
\(Hourly\ Rate = \$60\)
College Graduate
\(Charges = \$45\) --- first session
\(Hourly\ Rate = \$50\)
Required
Determine the number of hours they earn the same amount
Represent the hours with x
First, we need to calculate the total charges for the veteran tutor for x hours;
\(Total = 15 + 60x\)
Next, we need to calculate the total charges for the college graduate tutor for x hours;
\(Total = 45x + 50\)
For them to earn the same amount, we have:
\(15 + 60x = 45x + 50\)
Solving for x
\(60x - 45x = 50 - 15\)
\(15x = 35\)
Divide through by 15
\(x = \frac{35}{15}\)
\(x = 2.33\ hours\)
4x - 8 - 6x + 10 = ?
Answers
Answer:
-2x + 2
Step-by-step explanation:
Answer:
-2x+2
Step-by-step explanation:
This is the farthest this expression can be reduced to, there is no way to solve it
Hope this helps (:
Evaluate the expression when b=3 and x= -2.
-b + 8x
Answers
b=3 and x= -2.
-b + 8x
-3 + 8(-2)
-3 + -16
-19
have a great day :)
Janet averages 5 out of 8 baskets when shooting. Based on this information, if she takes 120 shots, how many will she make?
Answers
As the average is 5 out of 8 baskets. You multiply the total shots for 5/8 to find how many she makes:
\(120\cdot\frac{5}{8}=75\)Then, she makes 75 out of 120 baskets(y-7)^2=2y^2-4y+73 solve for y
Answers
Answer:
y=-4 or y=-6
Step-by-step explanation:
y^2-14y+49=2y^2-4y+73
y^2+10y+24=0
(y+4)(y+6)=0
y=-4 or y=-6
From nose to tail your first dog is 5 feet long. Your first dog is the length of your second dog. How many feet long f is your second dog
Answers
According to fraction and ratio, second dog is 3/2 feet long.
In math, what is a fraction?An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are divided. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.
First dog is 5 feet long.
then,
5 feet is equal to 4/5 of the second dog's length.
multiply both sides by 5/4.
5/4 x 5 feet is the second dog's length.
The second dog is 25/4 feet long.
The second dog is 6(1/4) feet long.
To know more about fraction visit:-
brainly.com/question/10354322
#SPJ4
Is it true that If A is n×n and detA = 2, then detA^3 = 6.
Answers
It is not true that if A is an n × n matrix with detA = 2, then detA³ = 6.
det(A³) = det(A × A × A) = det(A) × det(A) × det(A) = (det(A))³ = 2³ = 8
detA³ = 8, not 6.
The determinant of a matrix is a scalar value that encodes various properties of the matrix.
One of the properties is the volume scaling factor that is induced by the matrix transformation.
The determinant has the property that det(kA) = kⁿ × det(A) for any scalar k and n × n matrix A, where n denotes the dimension of the matrix.
Therefore, we have:
det(A³) = det(A × A × A) = det(A) × det(A) × det(A) = (det(A))³ = 2³ = 8
detA³ = 8, not 6.
The determinant of a matrix raised to a power is not simply obtained by raising the determinant to the same power.
The determinant of a matrix raised to a power can be obtained by raising the determinant of the matrix to the power and then multiplying by the scaling factor induced by the matrix transformation.
Specifically, for a matrix A with detA = 2 and an integer k, we have:
\(det(A^k) = (det(A))^k \times scaling factor induced by A^k\)
The scaling factor induced by \(A^k\) can be computed by considering the effect of \(A^k\) on the unit hypercube.
This calculation requires the use of linear algebra and is beyond the scope of this answer.
For similar questions on matrix
https://brainly.com/question/1279486
#SPJ11
Select the correct answer
Answers
Answer:
f(-7)=12
Step-by-step explanation:
f(-7)= 5-(-7)
f(-7)=5+7
f(-7)=12
Maya is playing a trivia game with multiple choice questions. Each question has
2 correct answers among 5 answer choices.
Maya has no idea what the answers to a certain question are, so she needs to choose two different answers at random.
What is the probability that Maya's first guess is CORRECT and her second guess is INCORRECT?
Round your answer to two decimal places.
Answers
The probability of both events occurring, we multiply the probabilities together is 0.30
How to find the probabilityFor the first guess, Maya has a 2 out of 5 chance of choosing a correct answer since there are 2 correct answers among 5 choices. This can be represented as a probability of 2/5.
For the second guess, after correctly selecting one answer, there are now 4 choices remaining, of which only 3 are incorrect.
Therefore, the probability of selecting an incorrect answer on the second guess is 3/4.
To find the probability of both events occurring, we multiply the probabilities together:
Probability = (2/5) * (3/4) = 6/20 = 0.3
Rounded to two decimal places, the probability is 0.30.
Learn more about probability at https://brainly.com/question/13604758
#SPJ1
Write the equation of a line passing through (-4,3) and perpendicular to 1x + 3y = 5.
Answers
To find the equation of a line that is perpendicular to another line, we need to use the fact that the slopes of perpendicular lines are negative reciprocals of each other. So the equation of the line passing through (-4,3) and perpendicular to 1x + 3y = 5 is y = 3x + 15.
First, we need to find the slope of the given line. We can rearrange the equation 1x + 3y = 5 to get it in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.
1x + 3y = 5
3y = -1x + 5
y = (-1/3)x + 5/3
So the slope of the given line is -1/3.
To find the slope of the line we want to write the equation for, we know that it must be the negative reciprocal of -1/3. So:
slope of perpendicular line = -1/(-1/3) = 3
Now we have the slope of the perpendicular line and a point it passes through (-4,3), so we can use point-slope form to write the equation:
y - y1 = m(x - x1)
where m is the slope we just found (3) and (x1, y1) is the given point (-4,3).
y - 3 = 3(x - (-4))
y - 3 = 3(x + 4)
y - 3 = 3x + 12
y = 3x + 15
So the equation of the line passing through (-4,3) and perpendicular to 1x + 3y = 5 is y = 3x + 15.
For more questions on slope - https://brainly.com/question/1884491
#SPJ11
Write the slope-intercept form of an equation of the line that passes through the given
point and is parallel to the graph of each equation.
(3, 2), y = x + 5
Answers
Answer:
The slope will be y=x-1 because it parallels to y=x+5 and hits point (3,2)
Step-by-step explanation:
Hope This Helped
You have one type of chocolate that sells for $2.50/1b and another type of chocolate that sells for $8.50/lb. You would like to have 36 lbs of a chocolate mixture that sells for $6.40/1b. How much of each chocolate will you need to obtain the desired mixture? You will need lbs of the cheaper chocolate and lbs of the expensive chocolate.
Answers
We have the next information
First type of chocolate $2.50 per lb
Second type of choclate 8.50 per lb
x= lbs of the cheaper chocolate
y=lbs of the expensive chocolate
36 total pounds
x+y=36
2.50(x)+8.50(y)=36(6.40)
2.5x+8.5y=230.4
then we solve the equation system
x+y=36 .....(1)
2.5x+8.5y=230.4 ....(2)
we clear x from the first equation
x=36-y
we substitute the equation above in the second equation
2.5(36-y)+8.5y=230.4
90-2.5y+8.5y=230.4
we clear y
6y=230.4-90
6y=140.4
y=140.4/6
y=23.4
then we substitute the value of y in the next equation
x=36-y=36-23.4
x=12.6
you will need 12.6 lbs of the cheaper chocolate and 23.4 lbs of the expensive chocolate
Quick question: Did I do this right?
Answers
Answer:
Yes. good job :)
keep up the good work 0u0
Step-by-step explanation:
Will give brainliest!!
Answers
Answer:
Answer is 21
order of operations
HELP PLEASE AND THANK YOU!!!!
Answers
Answer:
the answer is -2.1
Step-by-step explanation:
you get this by putting that -4 where the x is and solving so it would look something like this
1.7x+4.7 for x= -4
1.7(-4) + 4.7
-6.8 + 4.7
-2.1
Explanation:
I’ve had this question before! :)