8. Let the random variables X be the sum of independent Poisson distributed random variables, i.e.,...

Question

Question

8. Let the random variables X be the sum of independent Poisson distributed random variables, i.e., X = -1 Xi, where Xi is Po

math Statistics-And-Probability

Add a comment Improve this question Transcribed image text

Answer 1

Answer #1

Bay Map & X: : My_ce)= E(etxi) - Žetz Pex:xs) Zett par le biais Ricky] z endi Ž (dietye endet djet [: ] Y=0 Y! eniet 30% MGF

Add a comment

Answer 2

Similar Homework Help Questions

8. Let the random variables X be the sum of independent Poisson distributed random variables, i.e.,...

8. Let the random variables X be the sum of independent Poisson distributed random variables, i.e., X = 11-1Xị, where Xi is Poisson distributed with mean li. (a) Find the moment generating function of Xį. (b) Derive the moment generating function of X. (d) Hence, find the probability mass function of X.
new random variable X is distributed as Poisson) in this question. We create a U where...

new random variable X is distributed as Poisson) in this question. We create a U where its probability mass function is P(X u) u) P(X 1) P(U for u = 1,2,... (a) Show that e P(U u)= 1- e-A u!' for u 1,2,. (6 marks) expression for the moment generating function of U (7 marks (b) Derive an (c) Find the mean and variance of U (7 marks) new random variable X is distributed as Poisson) in this question. We...
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 X and Y be independent random variables uniformly distributed on the interval [1,2]. What is ...

Let X and Y be independent random variables uniformly distributed on the interval [1,2]. What is the moment generating function of X + 2Y? Let X and Y be independent random variables uniformly distributed on the interval [1,2]. What is the moment generating function of X + 2Y?
Let Y1, Y2, . .. , Yn be independent and identically distributed random variables such that...

Let Y1, Y2, . .. , Yn be independent and identically distributed random variables such that for 0 < p < 1, P(Yi = 1) = p and P(H = 0) = q = 1-p. (Such random variables are called Bernoulli random variables.) a Find the moment-generating function for the Bernoulli random variable Y b Find the moment-generating function for W = Yit Ye+ … + . c What is the distribution of W? 1.
I. Suppose that χ ~ Poisson (2) and y ~ Poisson (3) are independent random variables....

I. Suppose that χ ~ Poisson (2) and y ~ Poisson (3) are independent random variables. (a) Find the probability generating function of χ + y. (b) Use part (a) to find P(χ + y = 13). 2. Suppose that χ ~ Poisson (2) and y ~ Geom(0.25) are independent random variables. (a) Find the probability generating function of . (b) Find the probability generating function of χ + y.

Problem 41.3 Let X and Y be independent random variables each geometrically distributed with parameter p,...

Problem 41.3 Let X and Y be independent random variables each geometrically distributed with parameter p, i.e. p(1- p otherwise. Find the probability mass function of X +Y
7. Let X a be random variable with probability density function given by -1 < x < 1 fx(x) otherwise (a) Find the...

7. Let X a be random variable with probability density function given by -1 < x < 1 fx(x) otherwise (a) Find the mean u and variance o2 of X (b) Derive the moment generating function of X and state the values for which it is defined (c) For the value(s) at which the moment generating function found in part (b) is (are) not defined, what should the moment generating function be defined as? Justify your answer (d) Let X1,...
Question 3 [17 marks] The random variable X is distributed exponentially with parameter A i.e. X~...

Question 3 [17 marks] The random variable X is distributed exponentially with parameter A i.e. X~ Exp(A), so that its probability density function (pdf) of X is SO e /A fx(x) | 0, (2) (a) Let Y log(X. When A = 1, (i) Show that the pdf of Y is fr(y) = e (u+e-") (ii) Derive the moment generating function of Y, My(t), and give the values of t such that My(t) is well defined. (b) Suppose that Xi, i...

(1 point) In Unit 3, I claimed that the sum of independent, identically distributed exponential r...

(1 point) In Unit 3, I claimed that the sum of independent, identically distributed exponential random variables is a gamma random variable. Now that we know about moment generating functions, we can prove it. Let X be exponential with mean A 4. The density is 4 a) Find the moment generating function of X, and evaluate at t 3.9 The mgf of a gamma is more tedious to find, so l'll give it to you here. Let W Gamma(n, A...

8. Let the random variables X be the sum of independent Poisson distributed random variables, i.e.,...

Homework Answers