(a) State the Central Limit Theorem. (b) Consider the random variable Y with uniform distribution: f(y) = - {017-201 if 0₁ ≤ y ≤ 0₂ elsewhere = Show that the moment generating function E(ext)

Answers

Answer 1

The Central Limit Theorem states that the sum or average of a large number of independent and identically distributed random variables tends to follow a normal distribution, regardless of the shape of the original distribution.

This theorem is widely used in statistics and probability theory.The moment generating function (MGF) is a function that uniquely determines the probability distribution of a random variable.

To find the MGF for the random variable Y with a uniform distribution, we can use the formula:

M_Y(t) = E(e^(tY)) = ∫(e^(ty) * f(y)) dy

where f(y) is the probability density function of Y.

For the given uniform distribution with f(y) = - {017-201 if 0₁ ≤ y ≤ 0₂ elsewhere, we can split the integral into two parts:

M_Y(t) = ∫(e^(ty) * (-0.17)) dy, for 0₁ ≤ y ≤ 0₂

+ ∫(e^(ty) * 0) dy, elsewhere

Simplifying the first integral, we have:

M_Y(t) = -0.17 * ∫(e^(ty)) dy, for 0₁ ≤ y ≤ 0₂

Integrating e^(ty) with respect to y, we get:

M_Y(t) = -0.17 * [(e^(ty)) / t]₁₀₁

Substituting the limits of integration, we have:

M_Y(t) = -0.17 * [(e^(t0₂) - e^(t0₁)) / t]

Simplifying further, we obtain the moment generating function E(ext):

M_Y(t) = -0.17 * [(e^(t0₂) - e^(t0₁)) / t]

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Related Questions

Boar’s Head turkey costs $5.15 per pound. Mary needs to purchase 2.6 pounds for her family picnic. What is her total cost at the deli counter?

Answers

Answer:

13.34

Step-by-step explanation:

5.15+5.15=10.30

+3.04=13.34

Answer:

Step-by-step explanation:

13.39 dollar

bill has three one-piece jumpsuits, five pairs of work pants, and eight work shirts. he wears either a jumpsuit or pants and a shirt to work. how many different possible outfits does he have?

Answers

Bill has a total of 3 one-piece jumpsuits, 5 pairs of work pants, and 8 work shirts. To find the number of possible outfits he can wear to work, we can use the multiplication principle.

First, we need to determine how many choices Bill has for his top and bottom. He can either wear a jumpsuit or a combination of pants and a shirt. Therefore, he has 3 + (5 x 8) = 43 choices for his top and bottom.

Next, we can use the multiplication principle to determine the total number of possible outfits he can wear. Since he has 43 choices for his top and bottom, and each outfit combination is independent of the others, we can multiply the number of choices for his top and bottom by the number of one-piece jumpsuits he has.

Therefore, Bill has a total of 43 x 3 = 129 possible outfits he can wear to work.

In summary, Bill has 3 one-piece jumpsuits, 5 pairs of work pants, and 8 work shirts. He can wear either a jumpsuit or pants and a shirt to work. Using the multiplication principle, we determined that he has a total of 129 possible outfits he can wear.

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-x^2-3x-2 (i think this is trinomials, please help, I don't know how to do negatives :)

Answers

Answer:

$(-1)(x+1)(x+2)$

Step-by-step explanation:

$-x^2-3x-2\\$

Factor out the (-1)

$(-1)(x^2 + 3x + 2)$

Factor completely.

$(-1)(x+1)(x+2)$

The annual snowfall in city a is 69.8 inches. this is 14.5 inches more than times the snowfall in city b. find the annual snowfall for city b.

Answers

The annual snowfall for City B is approximately 4.81 inches.

To find the annual snowfall for City B, we need to solve the equation given in the question: 69.8 = 14.5x, where x represents the snowfall in City B.

This simplifies to:
69.8 / 14.5 = x

This simplifies to:
4.81 ≈ x

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find the formula for the mth term. the mth term of the sequence is 1536. find the value of m

Answers

Answer:

is given that the first term of G.P is a

=3 and the second term is a

=6, therefore,

We know that the formula for the nth term of an G.P is T

=ar

n−1

, where a is the first term, r is the common ratio.

It is given that the first term is a=3, the nth term is T

=1536 and the common ratio is r=2, thus,

=ar

n−1

⇒1536=3×(2)

n−1

⇒

1536

n−1

⇒2

n−1

=512

⇒2

n−1

⇒n−1=9

⇒n=9+1=10

Hence, the 10th term is 1536.

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Answers

Answer:

1.21...

Step-by-step explanation:

Are you sure you wrote the equation right? Just a little question but that should be the answer!

Joseph spends 12 hours a day playing amoung us . If Joseph plays 13 games in two hours , how many games does he play in a day ? How many games does he play per hour ?

Answers

Answer:

2hours = 13 games 12 divided by 2

x 6

--------

joseph plays 78 matches of among us a day

what should be added to 1 upon 4 to get 3 upon 4

Answers

Answer:

1/2

Step-by-step explanation:

1/4 + x = 3/4

x = 3/4 - 1/4

x = 2/4 = 1/2

Find the next four terms in the arithmetic sequence 1/4, 3/4, 5/4

Answers

Answer:

7/4, 9/4, 11/4, 13/4

Step-by-step explanation:

+ In an arithmetic sequence, to find the pattern you must subtract a term from the term after it to find the common difference.

3/4 subtracted from 5/4 is 2/4

1/4 subtracted from 3/4 is 2/4

+ So the common difference is 2/4 (Aka 1/2, but you want to keep the same denominator)

+ Therefore, between each new term, you add 2/4

1/4, 3/4, 5/4, 7/4, 9/4, 11/4, 13/4... and so on

a cookie manufacturer sells boxes of cookies that claim to weigh 16 ounces on the packaging. due to variation in the manufacturing process, the weight of the manufactured boxes follows a normal distribution with a mean of 16 ounces and a standard deviation of 0.25 ounce. the manufacturer decides it does not want to sell any boxes with weights below the 1st percentile so as to avoid negative customer responses. what is the minimum acceptable weight, in ounces, of a box of cookies? round your answer to two decimal places.

Answers

Rounding to two decimal places, the minimum acceptable weight of a box of cookies is 15.42 ounces.

weight of the boxes of cookies follows a normal distribution with a mean of 16 ounces and a standard deviation of 0.25 ounces.

To find the minimum acceptable weight of a box of cookies, we need to find the value that corresponds to the 1st percentile of the normal distribution.

Using a standard normal distribution table or calculator, we find that the z-score corresponding to the 1st percentile is approximately -2.33.

We can use the formula z = (x - μ) / σ, where x is the minimum acceptable weight, μ is the mean, and σ is the standard deviation, to solve for x.

Plugging in the values, we get:

-2.33 = (x - 16) / 0.25

Solving for x, we get:

x = -2.33 * 0.25 + 16 = 15.4175

Rounding to two decimal places, the minimum acceptable weight of a box of cookies is 15.42 ounces.

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A communications tower is located at the top of a steep hill, as shown. The angle of inclination of the hill is 58°. A guy wire is to be attached to the top of the tower and to the ground, 175 m downhill from the base of the tower. The angle in the figure is determined to be 13°. Find the length of cable required for the guy wire. (Round your answer to the nearest meter.)

Answers

Answer:

ii think that the figure will be determined by 13#

Step-by-step explanation:

you have to round up to the nearest meter

pls help asap if you can!!!!!

Answers

Answer:

x = 24

Step-by-step explanation:

if a and b are parallel then

62 and 5x - 2 are same- side interior angles and sum to 180° , that is

5x - 2 + 62 = 180

5x + 60 = 180 ( subtract 60 from both sides )

5x = 120 ( divide both sides by 5 )

x = 24

thus for a to be parallel to b , then x = 24

Help me very fast!!!!!!! Damon’s car can go an average of 18 miles on each gallon of gas.

Choose the equation that models the situation, where m represents the number of miles and g represents the number of gallons of gas.

Answers

Answer:

m= 18g

Step-by-step explanation:

m = 18 × g

PLEASE SOMEONE HELP
solve the equations using substitution method and SHOW YOUR WORK
A. y = 2x + 1
5x + y = 15

B. y = x + 7
4x + 3y = -7

C. y = 1
6x - 8y = 28

D. 2x - 3y = 16
4x + y = 4

Answers

Infinity Many Solutions

- Harvard university professor

find the z value for 0.99 if e O¨zlem likes jogging 3 days of a week. She prefers to jog 3 miles. For her 95 times, the mean wasx¼ 24 minutes and the standard deviation was S¼2.30 minutes. Let μ be the mean jogging time for the entire distribution of O¨zlem’s 3 miles running times over the past several years. How can we find a 0.99 confidence interval for μ?.
likes jogging 3 days of a week. She prefers to jog 3 miles. For her 95 times, the mean wasx¼ 24 minutes and the standard deviation was S¼2.30 minutes. Let μ be the mean jogging time for the entire distribution of O¨zlem’s 3 miles running times over the past several years. How can we find a 0.99 confidence interval for μ
a) What is the table value of Z for 0.99? (Z0.99)? (b) What can we use for σ ? (sample size is large) (c) What is the value of? Zcσffiffin p (d) Determine the confidence interval level for μ.

Answers

a. The table value of z 0.99 is given as 2.58.

b. we use σ = 2.30 minutes.

c. The value of Z is given as 0.609.

d. The confidence interval is (23.391, 24.609) minutes.

How to solve for the z critical value

a) To find the z-score for a 0.99 confidence interval, we need to find the z-score that leaves 0.5% (since it's two-tailed, we split the 1% or 0.01 of the data that's not within the confidence interval into two) in each tail. The z-score for 0.995 (0.5% in the upper tail) is approximately 2.58 in standard normal distribution tables. So, Z_0.99 is 2.58.

b) Therefore, we use σ = 2.30 minutes.

c) The standard error of the mean (SE) is given by σ/√n, where n is the sample size.

Here, σ = 2.30 minutes and n = 95.

Therefore, SE = σ/√n

= 2.30/√95

= 0.236 minutes.

Multiply this by the z-score to find Z * σ/√n.

Therefore, Z * σ/√n = 2.58 * 0.236 ≈ 0.609.

d) The 0.99 confidence interval for μ

Here, x is the sample mean which is 24 minutes.

So the confidence interval is approximately

= (24 - 0.609, 24 + 0.609)

= (23.391, 24.609) minutes.

This is the range of values we are 99% confident that the true population mean (μ) falls in.

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This is to get easy points but to also be kind
If Carmen drives 17.5 miles to a grocery store and 17.5 miles back then can’t find what she needs so she drive 12.5 miles to a gas station and 12.5 back how many miles did she drive.

I will be giving points out for being on this app so be on the lookout

Answers

Answer:

60 miles

Step-by-step explanation:

Distance travelled :

2 x Distance to grocery + 2 x Distance to gas station2(17.5) + 2(12.5)35 + 2560 miles

Which rational expression has a value of 0 when x = –2?
on ed

Answers

The rational expression has a value of 0 when x = 2 is shown by option B

What is the rational expression?

A rational expression is a mathematical expression that represents a ratio of two polynomial expressions. It is in the form of P(x)/Q(x), where P(x) and Q(x) are polynomials, and Q(x) is not equal to zero.

Rational expressions are commonly used in algebra to represent relationships, solve equations, and perform calculations involving variables.

Let us look at the values;

$7x - 5/x^2 + \\7(2) - 5/(2)^2$

= 9/4

-3x + 6/8x + 9

-3(2) + 6/8(2) + 9

= 0

-5x + 2/x - 2

-5(2) + 2/2 - 2

= ∞

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Missing parts;

Which rational expression has a value of 0 when x = 2 ? A) 7x -5/x2 + 10 B) -3x +6/8x-9 C) -5x + 8 / x-2

A local company employs a varying number of employees each year, based on its needs. The labor costs for the company include a fixed cost of $44,604.00 each year, and $27,396.00 for each person employed for the year. For the next year, the company projects that labor costs will total $1,715,760.00. How many people does the company intend to employ next year?
A.
731
B.
125
C.
61
D.
31

Answers

Answer:

Step-by-step explanation:

P × R × T÷ 100

1,715,760.00×27,396.00×44,604.00÷100

2.096609278659÷100

20,966,092,786,598.4

=31

-102 = -8(6 – 4x) – 5x

Answers

Answer:

x= -2

Step-by-step explanation:

Hope this helps.

Answer:

-102 = (-8×6 -8×-4x) -5x ( this is only for explanation write only this way as given below)

-102 = -48+32x -5x

-102 = -48+27x

-102+48= 27x

-54 = 27x

x = -54/27

x = -2 Ans

Hope you like it!

write the equation in slope-intercept form : 3x-9y=36

Answers

Answer:

y = 1/3x -4

Step-by-step explanation:

Solve for y

3x-9y = 36

Subtract 3x

3x -3x-9y = -3x +36

-9y = -3x +36

Divide by -9

-9y/-9 = -3x/-9 + 36/-9

y = 1/3x -4

This is in slope intercept form ( y = mx+b) where m is the slope and b is the y intercept

Slope intercept form: y = mx + b

Solve for y:

3x - 9y = 36

~Subtract 3x to both sides

3x - 3x - 9y = 36 - 3x

~Simplify

-9y = 36 - 3x

~Divide -9 to both sides

-9y/-9 = 36/-9 - 3x/-9

~Simplify

y = -4 + 1/3x

Therefore, the answer is y = 1/3x - 4

Best of Luck!

make t the subject of k= t-e/2

Answers

Answer:

$t=k+\frac{e}{2}$

Step-by-step explanation:

$k=t-\frac{e}{2}\\t=k+\frac{e}{2}$

Will mark brainly
ASAP

Answers

The answer is 56 since complementary angles add up to 90 degrees and one of them is 34 degrees

Which of the following is most likely to be a relative minimum for this graph?

Answers

Answer: A (3, -4)

Step-by-step explanation:

A minimum is at the lowest point on the parabola. The minimum and maximum can be seen by looking at the vertex.

If you go right 3 spaces on the x-axis horizontally, then down 4 spaces vertically on the y-axis you get (3, -4).

4 is negative because you are going down below the x-axis.

Consider the following relation: {(1, 3), (2, 7), (3, 11), (4, 15)} The above relation The domain is: The range is:

Answers

The domain of the given relation is {1,2,3,4} and the range of the given relation is {3,7,11,15}.

Given relation:-

{(1, 3), (2, 7), (3, 11), (4, 15)}

We know that, in a relation, the x coordinate represents the input of the relation and y coordinate represents the output of the relation.

The input value is a part of the domain and the output value is a part of the range.

Hence, the domain of the relation is {1,2,3,4} and the range of the given relation is {3,7,11,15}.

Domain

The domain of a relation is the set of the initial elements of all the ordered pairs of the relation.

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!Help Please!
Find the volume of this cylinder

Answers

Answer:

V~1911

Step-by-step explanation:

7^2=49

3*49=147

147=1911

V~1911

let x(t) = cos(75t). if we sample x(t) at the nyquist frequency, what is the resulting discrete frequency

Answers

If we sample the function x(t) = cos(75t) at the Nyquist frequency, the resulting discrete frequency would be half of the Nyquist frequency, which is equal to half of the highest frequency component in the continuous signal.

In this case, the highest frequency component in x(t) is 75 Hz, as determined by the coefficient of t in the cosine function. According to the Nyquist-Shannon sampling theorem, to accurately represent a signal, the sampling frequency must be at least twice the highest frequency component. Therefore, the Nyquist frequency in this scenario would be 2 * 75 Hz = 150 Hz.

Since we are sampling at the Nyquist frequency, the resulting discrete frequency would be half of the Nyquist frequency, which is 150 Hz / 2 = 75 Hz. Hence, when sampling x(t) at the Nyquist frequency, the resulting discrete frequency would be 75 Hz.

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This is Evaluating Functions.Replace the X values with the number in the question ("Find f( )" )

Answers

Given the following function:

f(x) = 3x - 3

Let's determine the value at f(-3),

This means that we will be replacing all x variables of f(x) by -3.

We get,

f(x) = 3x - 3

f(-3) = 3(-3) - 3

= -9 - 3

f(-3) = -12

Therefore, f(-3) = -12

Given the following function:

f(x) = 3x - 3

Let's determine the value at f(-3),

This means that we will be replacing all x variables of f(x) by -3.

We get,

f(x) = 3x - 3

f(-3) = 3(-3) - 3

= -9 - 3

f(-3) = -12

Therefore, f(-3) = -12

Suppose a meal consists of one sandwich, one side order and one beverage. What is the most
expensive meal you can purchase? How much does it cost?

Hamburger $3.25
Bacon Cheeseburger $4.75
Chicken Fajita Taco $3.50
French Fries, Small $1.55
French Fries, Large $1.90
Onion Rings $2.40
Cole Slaw $1.45
Soft Drink, Small $1.30
Soft Drink, Large $1.65
Milkshake $3.25
Juice $1.80

Answers

$26.8 is the total cost and Chicken Fajita Taco is the most

expensive meal .

What in mathematics is a linear equation?

There are only one or two variables in a linear equation. No variable can be multiplied by a number larger than one or used as the denominator of a fraction in a linear equation. All of the points fall on the same line when you identify the values that together make a linear equation true and plot those values on a coordinate grid.

Hamburger + Bacon Cheeseburger + Chicken Fajita Taco + French Fries, Small + French Fries, Large + Onion Rings + Cole Slaw + Soft Drink, Small + Soft Drink, Large + Milkshake + Juice

= $3.25 + $4.75 + $3.50 + $1.55 + $1.90 + $2.40 + $1.45 + $1.30 + $1.65 + $3.25 + $1.80

= $26.8

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solve for$5^{3x-2} = 7^{x+2}$

Answers

Answer:

x ≈ 2.467

Step-by-step explanation:

You want the solution to 5^(3x -2) = 7^(x +2).

Logs

Logarithms turn an exponential problem into a linear problem. Taking logs, we have ...

(3x -2)·log(5) = (x +2)·log(7)

x(3·log(5) -log(7)) = 2(log(7) +log(5)) . . . . . separate variables and constants

x = log(35²)/log(5³/7) = log(1225)/log(125/7) . . . . divide by x-coefficient

x ≈ 2.46693

Additional comment

A graphing calculator can solve this nicely as the x-intercept of the function f(x) = 5^(3x-2) -7^(x+2). Newton's method iteration is easily performed to refine the solution to calculator precision.

$solve for[tex]5^{3x-2} = 7^{x+2}[/tex]$

What is the formula for calculating angle?

Answers

Angles Formulas at the center of a circle can be expressed as:

Central angle, θ = (Arc length × 360º)/(2πr) degrees

Sum of Interior angles=180°(n-2)

The angles formulas are used to find the measures of the angles. An angle is formed by two intersecting rays, called the arms of the angle, sharing a common endpoint.

The corner point of the angle is known as the vertex of the angle. The angle is defined as the measure of the turn between the two lines.

There are various types of formulas for finding an angle; some of them are the central angle formula, double-angle formula, etc...

We use the central angle formula to determine the angle of a segment made in a circle.

We use the sum of the interior angles formula to determine the missing angle in a polygon.

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What is the function of splitting? The table represents equivalent ratios. Which statements are true? (pick two please!)The missing y-value is -4The missing x-value is 2The ordered pair (-1,2) is part of the ratio table.The points will be in quadrants | and ||| Identify the source described as primary secondary and Tertiary an original oil Secondary PrimaryTertiary Graph the line with slope -1/2passing through the point (4, -3). The reaction rate constant is determined to be 0.012 M-1 s-1. If after 27 minutes the amount of A left is 0.048 M. What was the initial concentration of A?0.0492.53e160.7219.49 At a hamburger stand, a burger is $6, a drink is $3, and there iscurrently a special offer for a $1 discount on every order.Write an equation that represents the total cost C of b burgersand d drinks. which weighs more: a puppy the weighs 8.5 kilograms or a baby that weighs 11 pounds? How many moles of CaCl would there be in 42 mL of 2.09 M aqueous CaCl solution?3 significant figures !NEED ANSWER ASAP! Two classes of elementary school students were asked what activity they want to do during recess. Each student selects one recess option. The table summarizes the recess preference of each student in the class.What is the probability that a student selected at random prefers to play tag at recess? In each of the following equations, what hybridization change, if any, occurs for the underlined atom?A. BF3 +NaFNaBF4B. S2 +1/2O2SO3C. ethene(CH2=CH2)+H2CH2BrCH2Br properties of a homogeneous mixture what is n? 2(n+5)=-2 What was the main reason that most Mississippi landowners resisted the nations move to outlaw slavery? are 3(2x+11) and (3x+15)(2) equivalent looooooooooooooooootttttttsss offffffffffffffffffff pointtttttttttttttttttttssssssssssssssssssssssssss What the slope intercept form of (-3,3) and (3,-3) 4) the volumes of soda in quart soda bottles are normally distributed with a mean of 32.3 oz and a standard deviation of 1.2 oz. what percentage of bottles contain less than 32 oz of soda? If you know that 84 is 70% of the whole, how can you use proportional reasoning to determine the whole?A: 70100 shows 70% as a ratio. The ratio 84x compares 84 to the whole, x. Write an equation so that the first ratio is equal to the second ratio. Solve for x : x = 120.B: 70100 shows 70% as a ratio. The ratio 84x compares 84 to the whole, x. Write an equation so that the first ratio is multiplied by the second ratio. Solve for x : x = 58.8.C: 70100 shows 70% as a ratio. The ratio x84 compares 84 to the whole, x. Write an equation so that the first ratio is multiplied by the second ratio. Solve for x : x = 120.D: 70100 shows 70% as a ratio. The ratio x84 compares 84 to the whole, x. Write an equation so that the first ratio is equal to the second ratio. Solve for x : x = 58.8. When a firm uses third-degree price discrimination, the group ofconsumers with _____ demand would face the highest prices.unitary elasticperfectly elasticlow elasticity ofhigh elasticity of Yo _____ la televisin. options:a) vemosb) venc) vesd) veo