Calculus and Above

Calculus Questions? Ask a Mathematician for Answers ASAP

Connect one-on-one with {0} who will answer your question

I am preparing for a...

I am preparing for a probability theory test and I am having problems with MGF's these are some examples from previous exams which I would like solutions for along with explanations to help me study. There is 5 Q's in total.

10. a)Y has moment generating function mY (z) = e^−8z+32z^2 . What is the

variance of Y ? What is P(Y ≤ −4)?

b)Use the moment generating function to derive the expected value of a

Poisson random variable with parameter λ = 1/3.

c)Let Y ∼ Uniform(α,β), α,β ∈ R and α β−Y}= 1/(1+y)

9. (a)

The random variable X has moment generating function

mX (t) = exp (−5t + 12t^2) .

If Z = 1/5 (X − 2), what are E(Z) and Var(Z)?

￼(b) Y is a random variable with moment generating function mY (t) = (1/(1 − 2t))^8 .

What are E(Y ) and Var(Y )?

8.

Let Z1 and Z2 be independent normal random variables where Z1 ∼ N(6,3^2) and Z2 ∼ N(4,1^2). Define Y1 = Z1 −Z2 and Y2 = 2(Z1) +3(Z2). Find the means and variances of the random variables Y1 and Y2. [6]

The random variable X has moment generating function mX (t) = exp(−7t + 18t^2).

If W = 1/5(X − 2) what are the expected value and variance of W?

10. (a)

The random variable X has moment generating function

mx(t)=(1−2t)^−15/2 .

If Z = 1/3(X + 3), what is the variance V(Z)?

￼(b) Y is a random variable with moment generating function mY (t) = (0.8 + 0.2e^t)^10 .

What is P(1≤Y ≤4)?

11. (a)

The random variable X takes the values 0, 1, 2 with probabilities 1/2 , 3/8, 1/8

respectively. Find the moment generating function for X and verify that

￼￼￼the second moment of X is 7/8.

[5]

(b)

The random variable Z has distribution function FZ (z) = 1 − exp(−5z) for z ∈ [0, ∞). Find the moment generating function for Z and verify

that the first moment of Z is 0.2.

[5]

10. a)Y has moment generating function mY (z) = e^−8z+32z^2 . What is the

variance of Y ? What is P(Y ≤ −4)?

b)Use the moment generating function to derive the expected value of a

Poisson random variable with parameter λ = 1/3.

c)Let Y ∼ Uniform(α,β), α,β ∈ R and α β−Y}= 1/(1+y)

9. (a)

The random variable X has moment generating function

mX (t) = exp (−5t + 12t^2) .

If Z = 1/5 (X − 2), what are E(Z) and Var(Z)?

￼(b) Y is a random variable with moment generating function mY (t) = (1/(1 − 2t))^8 .

What are E(Y ) and Var(Y )?

8.

Let Z1 and Z2 be independent normal random variables where Z1 ∼ N(6,3^2) and Z2 ∼ N(4,1^2). Define Y1 = Z1 −Z2 and Y2 = 2(Z1) +3(Z2). Find the means and variances of the random variables Y1 and Y2. [6]

The random variable X has moment generating function mX (t) = exp(−7t + 18t^2).

If W = 1/5(X − 2) what are the expected value and variance of W?

10. (a)

The random variable X has moment generating function

mx(t)=(1−2t)^−15/2 .

If Z = 1/3(X + 3), what is the variance V(Z)?

￼(b) Y is a random variable with moment generating function mY (t) = (0.8 + 0.2e^t)^10 .

What is P(1≤Y ≤4)?

11. (a)

The random variable X takes the values 0, 1, 2 with probabilities 1/2 , 3/8, 1/8

respectively. Find the moment generating function for X and verify that

￼￼￼the second moment of X is 7/8.

[5]

(b)

The random variable Z has distribution function FZ (z) = 1 − exp(−5z) for z ∈ [0, ∞). Find the moment generating function for Z and verify

that the first moment of Z is 0.2.

[5]

Show More

Show Less

Was this answer helpful?

Describe your issueThe assistant will guide you

Chat 1:1 with a tutorLicensed Experts are available 24/7

100% satisfaction guaranteeGet all the answers you need

Related Calculus and Above Questions

RandomCereal, the best cereal brand, has come up with a

RandomCereal, the best cereal brand, has come up with a holiday edition. Inde- pendently for each cereal box, the company either places a reindeer figurine in the box with probability 2/5, places an e… read more

Question 1: Two waves on one string are described by the

Question 1: Two waves on one string are described by the wave functionswhere x and y are in centimeters and t is in seconds. Find the superposition of the waves y1 and y2 at the points (a) x = 1.00 m… read more

A) Write an equation for the linear function that passes

A) Write an equation for the linear function that passes through (0,3) and (3,7)B) Write an equation for an exponential function that passes through (0,3) and (3,7) round your Constance to three decim… read more

3-1: Random variable X distributed Normal(16, 9) Compute

3-1: Random variable X distributed Normal(16, 9) Compute P[13 < X < 22] =#3-2: Random variable X distributed as Normal(8, 16), and Random variable Y distributed as Normal(4, 25), And X and Y are… read more

SHOW YOUR WORK #3-1: Random variable X distributed

SHOW YOUR WORK#3-1: Random variable X distributed Normal(16, 9) Compute P[13 < X < 22] =#3-2: Random variable X distributed as Normal(8, 16), and Random variable Y distributed as Normal(4, 25), … read more

Let X ∼Γ(α,β), which has p.d.f. fX(x)= βα xα−1e−βxI(0,∞)(x),

Let X ∼Γ(α,β), which has p.d.f. fX(x)= βα xα−1e−βxI(0,∞)(x), where Γ(ω):=∞vω−1e−vdv is the Γ(α) 0 Gamma function, for ω > 0. 1. Compute the moment generating function of X. [5 points] [Hint: 0∞… read more

I have two questions in advanced stochastic process

I have two questions in advanced stochastic process assignment nee help … read more

1. (a) Use the definition of moment generating functions to

1. (a) Use the definition of moment generating functions to show that if MX(t) is the mgf of a continuous random variable X, then if Y = (X+a)/b, MY (t) = e^(a/b)t MX(t/b) ￼￼ (b) Choose appropriate co… read more

1. An immigration-birth process with arrival rate λ and birth

1. An immigration-birth process with arrival rate λ and birth rate β may be described by the probability statement P(X(t +δt) = x + 1| X(t) = x) = (λ + βx)δt + 0(δt) Suppose that at time 0 the size of… read more

Dr. Rubin, Bob here with a follow up question from your answer

Dr. Rubin, Bob here with a follow up question from your answer last week. This is a new request so far as I'm concerned. Here's the request: I would like a formula solved for 'x' and for 'y' that allo… read more

I need to compare/analyse the following automated weighing

I need to compare/analyse the following automated weighing scale output: 1 sample A1 with 5127 subjects In order to determine if a faster feed-rate than that which is recommended, produces a result th… read more

Hello!I Hope this is the right category. The following is

Hello! I Hope this is the right category. The following is a mathematical logic question that is been bugging me for awhile: How long a list of non-equivalent pure monadic schemata containing only the… read more

The Pareto distribution, with parameters α and β, has pdf

The Pareto distribution, with parameters α and β, has pdf f(x)=(βα^β)/x^(β+1) ,α0. a)Verify that f(x) is a pdf. b) Derive the mean and variance of the distribution. c) Prove that variance does not exi… read more

Hi Ashok, I have 33 Questions based on all the questions

Hi Ashok, I have 33 Questions based on all the questions I have asked you over the past 8 weeks. Once I post the questions i will need the answers to the Multiple choice questions (24) within 3 hours … read more

In the following problems the function y1(x) is a solution

In the following problems the function y1(x) is a solution of the given differerential equation. Use the method of reduction of order to find a second solution y2(x): 1) (4x^2)y'' + y = 0 ; y1(x) = x^… read more

Give a method for generating a random variable having distribution

Give a method for generating a random variable having distribution function F (x) = 1 − exp(−αx^β ), 0 < x < ∞. A random variable having such a distribution is said to be a Weibull random variab… read more

Give a method for generating a random variable having distribution

Give a method for generating a random variable having distribution function F (x) = 1 − exp(−αx^β ), 0 < x < ∞. A random variable having such a distribution is said to be a Weibull random variab… read more

X are iid random variables with symmetrical distribution f(x),

X are iid random variables with symmetrical distribution f(x), mu and sigma. Minimize the sum of absolute value of (Xi - b) wrt b. b turns out to be the median but how do we get there?… read more

Disclaimer: Information in questions, answers, and other posts on this site ("Posts") comes from individual users, not JustAnswer; JustAnswer is not responsible for Posts. Posts are for general information, are not intended to substitute for informed professional advice (medical, legal, veterinary, financial, etc.), or to establish a professional-client relationship. The site and services are provided "as is" with no warranty or representations by JustAnswer regarding the qualifications of Experts. To see what credentials have been verified by a third-party service, please click on the "Verified" symbol in some Experts' profiles. JustAnswer is not intended or designed for EMERGENCY questions which should be directed immediately by telephone or in-person to qualified professionals.

Ask-a-doc Web sites: If you've got a quick question, you can try to get an answer from sites that say they have various specialists on hand to give quick answers... Justanswer.com.

JustAnswer.com...has seen a spike since October in legal questions from readers about layoffs, unemployment and severance.

Web sites like justanswer.com/legal

...leave nothing to chance.

...leave nothing to chance.

Traffic on JustAnswer rose 14 percent...and had nearly 400,000 page views in 30 days...inquiries related to stress, high blood pressure, drinking and heart pain jumped 33 percent.

Tory Johnson, GMA Workplace Contributor, discusses work-from-home jobs, such as JustAnswer in which verified Experts answer people’s questions.

I will tell you that...the things you have to go through to be an Expert are quite rigorous.

Wonderful service, prompt, efficient, and accurate. Couldn't have asked for more. I cannot thank you enough for your help.

Freshfield, Liverpool, UK

This expert is wonderful. They truly know what they are talking about, and they actually care about you. They really helped put my nerves at ease. Thank you so much!!!!

Los Angeles, CA

Thank you for all your help. It is nice to know that this service is here for people like myself, who need answers fast and are not sure who to consult.

Hesperia, CA

I couldn't be more satisfied! This is the site I will always come to when I need a second opinion.

Kernersville, NC

Just let me say that this encounter has been entirely professional and most helpful. I liked that I could ask additional questions and get answered in a very short turn around.

Woodstock, NY

Thank you so much for taking your time and knowledge to support my concerns. Not only did you answer my questions, you even took it a step further with replying with more pertinent information I needed to know.

Elkton, Maryland

He answered my question promptly and gave me accurate, detailed information. If all of your experts are half as good, you have a great thing going here.

Dallas, TX

< Previous | Next >

Mr. Gregory White

Master's Degree

114 satisfied customers

M.A., M.S. Education / Educational Administration

SusanAthena

Master's Degree

102 satisfied customers

Tutor for Algebra, Geometry, Statistics. Explaining math in plain English.

Dr Arthur Rubin

Doctoral Degree

97 satisfied customers

Ph.D. in Mathematics, 1978, from the California Institute of Technology, over 20 published papers

JACUSTOMER-yrynbdjl-

Master's Degree

42 satisfied customers

I have a MS in Mathematics and I have taught Mathematics for 10 years at the college level.

Don

Master's Degree

29 satisfied customers

M.S. Astronautical Engineering. Math/Sci/Comp Tutor

Kofi

PhD in Statistics

7,955 satisfied customers

Masters in Mathematics and Statistics

Sandhya_sharma

Master's Degree

5,547 satisfied customers

I hold M.Sc and M.Phil degrees in math and have several years of teaching experience.

< Previous | Next >

Disclaimer: Information in questions, answers, and other posts on this site ("Posts") comes from individual users, not JustAnswer; JustAnswer is not responsible for Posts. Posts are for general information, are not intended to substitute for informed professional advice (medical, legal, veterinary, financial, etc.), or to establish a professional-client relationship. The site and services are provided "as is" with no warranty or representations by JustAnswer regarding the qualifications of Experts. To see what credentials have been verified by a third-party service, please click on the "Verified" symbol in some Experts' profiles. JustAnswer is not intended or designed for EMERGENCY questions which should be directed immediately by telephone or in-person to qualified professionals.