4.6 Let Z1, Z2, ..., Za be a random sample from a Poisson distribution with mean...

Question

Question

4.6 Let Z1, Z2, ..., Za be a random sample from a Poisson distribution with mean j. (a) Show that the variance of Z, depends

math Statistics-And-Probability

Add a comment Improve this question Transcribed image text

Answer 1

Answer #1

Answar (2) From the given question Et ~P(M) So the proof of Zt is +(44) - (4)! ist [%t (84 --))= T 7+ (ze --)f (4) Zd=0 = Ź t F(E+)s Variance is independent of l. Where Hence to the fronsformation is {{4} → F{{{4}) where Flüe) = Ę 4 GB) (6) The Varta

Add a comment

Answer 2

Similar Homework Help Questions

Exercise 8.43. Let Z1, Z2,... . Zn be independent normal random variables with mean 0 and variance 1. Let (a) Using that Y is the sum of independent random variables, compute both the mean and varian...

Exercise 8.43. Let Z1, Z2,... . Zn be independent normal random variables with mean 0 and variance 1. Let (a) Using that Y is the sum of independent random variables, compute both the mean and variance of Y. (b) Find the moment generating function of Y and use it to compute the mean and variance of Y. Exercise 8.43. Let Z1, Z2,... . Zn be independent normal random variables with mean 0 and variance 1. Let (a) Using that Y...
Let Y1<Y2<...<Yn be the order statistics of a random sample of size n from the distribution...

Let Y1<Y2<...<Yn be the order statistics of a random sample of size n from the distribution having p.d.f f(x) = e-y , 0<y<, zero elsewhere. Answer the following questions. (a) decide whether Z1 = Y2 and Z2=Y4-Y2 are stochastically independent or not. (hint. first find the joint p.d.f. of Y2 and Y4) (b) show that Z1 = nY1, Z2= (n-1)(Y2-Y1), Z3=(n-2)(Y3-Y2), ...., Zn=Yn-Yn-1 are stocahstically independent and that each Zi has the exponential distribution.(hint use change of variable technique)
Let X1...Xn be independent, identically distributed random sample from a poisson distribution with mean theta. a....

Let X1...Xn be independent, identically distributed random sample from a poisson distribution with mean theta. a. Find the meximum liklihood estimator of theta, thetahat b. find the large sample distribution for (sqrt(n))*(thetahat-theta) c. Construct a large sample confidence interval for P(X=k; theta)

Suppose that Z1 and Z2 are uncorrelated random variables with zero mean and unit variance. Consider...

Suppose that Z1 and Z2 are uncorrelated random variables with zero mean and unit variance. Consider the process deﬁned by Yt = Z1 cos(ωt) + Z2 sin(ωt) + et where et ∼ iid N(0,σ2 e) and {et} is independent of both Z1 and Z2. Prove that {Yt} is stationary.
| Assume that Z1 and Z2 are two independent random variables that follow the standard normal...

| Assume that Z1 and Z2 are two independent random variables that follow the standard normal dist ribution N(0,1), so that each of them has the density 1 (z) ooz< oo. e '2т X2 X2+Y2 Let X 212,Y 2Z1 2Z2, S X2Y2, and R (a) Please find the joint density of (Z1, Z2). (b) From (a), please find the joint density of (X,Y) (c) From (b), please find the marginal densit ies of X and Y. (d) From (b) and...
Let Z1, Z2,.., Zn be independent Normal(0,1) random variables (a) Find the MGF for Z for...

Let Z1, Z2,.., Zn be independent Normal(0,1) random variables (a) Find the MGF for Z for all i (b) Find the MGF for (c) If n is even, find the PDF for Σ

and let X and S be sample mean be a random sample from N(u,0) 1. Let...

and let X and S be sample mean be a random sample from N(u,0) 1. Let are independent, follow the and sample variance, respectively. In order to show that X and S steps below X x-x2 , and show the joint pdf of 1-1) Use the change of variable technique X,X,,X n is (n 1s 202 1 f(F,x,) = n exp 202 a27 [Hint 1] Use Jacobian for n x n variable transformation [Hint 2] 4AT-r- des dis Je ddi...
and let X and S be sample mean be a random sample from N(u,0) 1. Let...

and let X and S be sample mean be a random sample from N(u,0) 1. Let are independent, follow the and sample variance, respectively. In order to show that X and S steps below X x-x2 , and show the joint pdf of 1-1) Use the change of variable technique X,X,,X n is (n 1s 202 1 f(F,x,) = n exp 202 a27 [Hint 1] Use Jacobian for n x n variable transformation [Hint 2] 4AT-r- des dis Je ddi...
2. Let Z1, Z2, Zn be independent Normal(0,1) random variables (a) Find the MGF for Z...

2. Let Z1, Z2, Zn be independent Normal(0,1) random variables (a) Find the MGF for Z for all i (b) Find the MGF for Σ_1 Z (c) If n is even, find the PDF for ΣΙ_1 z?

4 points) Let Z1,Z2,...,Z1 be 11 independent N(O, 1) variables, and let Provide answers to the...

4 points) Let Z1,Z2,...,Z1 be 11 independent N(O, 1) variables, and let Provide answers to the following to two decimal places Part a) Evaluate the moment generating function Mz2 (t) of Z2 at the point 0.23 Part b) Evaluate the moment generating function My(t) of Y at the point t = 0.31 . Part c) Find the mean of Y. Part d) Find the variance of Y.

4.6 Let Z1, Z2, ..., Za be a random sample from a Poisson distribution with mean...

Homework Answers

Add Answer to:
4.6 Let Z1, Z2, ..., Za be a random sample from a Poisson distribution with mean...

Post as a guest

Earn Coins

Exercise 8.43. Let Z1, Z2,... . Zn be independent normal random variables with mean 0 and variance 1. Let (a) Using that Y is the sum of independent random variables, compute both the mean and varian...

Let Y1<Y2<...<Yn be the order statistics of a random sample of size n from the distribution...

Let X1...Xn be independent, identically distributed random sample from a poisson distribution with mean theta. a....

Suppose that Z1 and Z2 are uncorrelated random variables with zero mean and unit variance. Consider...

| Assume that Z1 and Z2 are two independent random variables that follow the standard normal...

Let Z1, Z2,.., Zn be independent Normal(0,1) random variables (a) Find the MGF for Z for...

and let X and S be sample mean be a random sample from N(u,0) 1. Let...

and let X and S be sample mean be a random sample from N(u,0) 1. Let...

2. Let Z1, Z2, Zn be independent Normal(0,1) random variables (a) Find the MGF for Z...

4 points) Let Z1,Z2,...,Z1 be 11 independent N(O, 1) variables, and let Provide answers to the...

4.6 Let Z1, Z2, ..., Za be a random sample from a Poisson distribution with mean...

Homework Answers

Add Answer to: 4.6 Let Z1, Z2, ..., Za be a random sample from a Poisson distribution with mean...

Post as a guest

Earn Coins

Add Answer to:
4.6 Let Z1, Z2, ..., Za be a random sample from a Poisson distribution with mean...