Question

Let S4 = X1 + ... + X4 is the sum of 4 independent random variables,...

Let S4 = X1 + ... + X4 is the sum of 4 independent random variables, and each Xi is exponential with
λ = 3. Find the moment generating function m(t) for S4. Also find m′(0) and m′′(0）
Math   Statistics-And-Probability   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

MGF of Exponential

We will use the two information above,

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
1) Let the random variables ? be the sum of independent Poisson distributed random variables, i.e.,...
1) Let the random variables ? be the sum of independent Poisson distributed random variables, i.e., ? = ∑ ? (top) ?=1(bottom) ?? , where ?? is Poisson distributed with mean ?? . (a) Find the moment generating function of ?? . (b) Derive the moment generating function of ?. (c) Hence, find the probability mass function of ?. 2)The moment generating function of the random variable X is given by ??(?) = exp{7(?^(?)) − 7} and that of ?...
Let X1, X2, X3, and X4 be mutually independent random variables from the same distribution. Let...
Let X1, X2, X3, and X4 be mutually independent random variables from the same distribution. Let S = X1 + X2 + X3 + X4. Suppose we know that S is a Chi-Square random variable with 2 degrees of freedom. What is the distribution of each of the Xi?
Let X1, X2,... be a sequence of independent random variables distributed exponentially with mean 1. Suppose...
Let X1, X2,... be a sequence of independent random variables distributed exponentially with mean 1. Suppose that N is a random variable, independent of the Xi-s, that has a Poisson distribution with mean λ > 0. What is the expected value of X1 + X2 +···+ XN2? (A) N2 (B) λ + λ2 (C) λ2 (D) 1/λ2
Let ? and ? be two independent random variables with moment generating functions ?x(?) = ?t^2+2t...
Let ? and ? be two independent random variables with moment generating functions ?x(?) = ?t^2+2t and ?Y(?)=?3t^2+t . Determine the moment generating function of ? = ? + 2?. If possible, state the distribution name (and include parameter values) of the distribution of ?.
Let x1, x2 x3 ....be a sequence of independent and identically distributed random variables, each having...
Let x1, x2 x3 ....be a sequence of independent and identically distributed random variables, each having finite mean E[xi] and variance Var（xi）. a）calculate the var （x1+x2） b）calculate the var（E[xi]） c） if n-> infinite, what is Var（E[xi]）？
Let X1,...,X99 be independent random variables, each one distributed uniformly on [0, 1]. Let Y denote...
Let X1,...,X99 be independent random variables, each one distributed uniformly on [0, 1]. Let Y denote the 50th largest among the 99 numbers. Find the probability density function of Y.
Suppose X1, X2, X3, and X4 are independent and identically distributed random variables with mean 10...
Suppose X1, X2, X3, and X4 are independent and identically distributed random variables with mean 10 and variance 16. in addition, Suppose that Y1, Y2, Y3, Y4, and Y5are independent and identically distributed random variables with mean 15 and variance 25. Suppose further that X1, X2, X3, and X4 and Y1, Y2, Y3, Y4, and Y5are independent. Find Cov[bar{X} + bar{Y} + 10, 2bar{X} - bar{Y}], where bar{X} is the sample mean of X1, X2, X3, and X4 and bar{Y}...
Let X1 and X2 be two independent geometric random variables with the probability of success 0...
Let X1 and X2 be two independent geometric random variables with the probability of success 0 < p < 1. Find the joint probability mass function of (Y1, Y2) with its support, where Y1 = X1 + X2 and Y2 = X2.
Let X1 , X2 , X3 , X4 be a random sample of size 4 from...
Let X1 , X2 , X3 , X4 be a random sample of size 4 from a geometric distribution with p = 1/3. A) Find the mgf of Y = X1 + X2 + X3 + X4. B) How is Y distributed?
Let X1, X2 be two normal random variables each with population mean µ and population variance...
Let X1, X2 be two normal random variables each with population mean µ and population variance σ2. Let σ12 denote the covariance between X1 and X2 and let ¯ X denote the sample mean of X1 and X2. (a) List the condition that needs to be satisfied in order for ¯ X to be an unbiased estimate of µ. (b) [3] As carefully as you can, without skipping steps, show that both X1 and ¯ X are unbiased estimators of...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT