Problem 3. Suppose that X and Y are independent Poisson random variables with param-eters A and μ, respectively. Find the distribution of X+Y. Prove that the conditionaldistribution of X, given that X + Y = n, is binomial with parameters n and λ/(\+µ). (Fortwo random variables Z and T, the conditional distribution of Z given T is given byPz|T(z|t) = P(Z = z |T = t),for all t such that P(T = t) > 0.)

Answered: Image /qna-images/answer/5c6c3d3a-0537-4c51-b746-dd039279fa3c.jpg

Answered: roblem 3. Suppose that X and Y are…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Similar questions

Show that, if X1 and X2 are independent random variables with geometric distributions of aparameter p, then Y = X1 + X2 has a negative binomial distribution with parameters p andk = 2.
Suppose X and Y are the random variables with joint PMF given by: X/Y 11.2 5.75 -3 0 0.07 -2 0.2 0.08 -1 0.1 0.1 0 0.15 0.1 1 0 0.2 a.) Compute E(X2)
A simple random sample of size 200 is taken from a much larger group of male wrestlers prior to a competition. The average weight in the sample is 190 pounds, with an SD of 20 pounds. The average weight of the population is estimated to be 190 pounds, and this estimate is likely to be off by about _______.
A poisson random variables has f(x,3)= 3x e-3÷x! ,x= 0,1.......,∞. find the probabilities for X=0 1 2 3 4 and also find mean and variance from f(x,3).?
If X and Y are independent Poisson random variables with E[X] = 3 and E[Y] = 2, what is P[ X = 2 | X + Y = 4 ]?
An alternative proof of Theorem 2 may be based on the fact that if X1, X2, ..., and Xn are independent ran-dom variables having the same Bernoulli distribution with the parameter θ, then Y = X1 + X2 +···+ Xn isa random variable having the binomial distribution withthe parameters n and θ.Verify directly (that is, without making use of the factthat the Bernoulli distribution is a special case of thebinomial distribution) that the mean and the variance ofthe Bernoulli distribution are μ = θ and σ2 = θ (1 − θ
Suppose again that Y is a normally distributed random variable with mu = 10 and sigma = 2. The probability that Y will assume a value between 7 and 14 is
Problems 5 and 6 refer to the discrete random variables X and Y whose joint distribution is given in the following table, so P(X = 1 and Y = -1) = 1/4, P(X = 1 and Y = 1) = 0, etc. Problem 5: Compute the marginal distributions of X and Y, and use these to compute E(X), E(Y), Var(X), and V ar(Y). Problem 6: Compute Cov(X, Y) and the correlation ρ for the random variables X and Y. Are X and Y independent? Y= -1 Y =0 Y =1 X =1 1/4 1/8 0 X =2 1/16 1/16 1/8 X =3 1/16 1/16 1/4
If X is Poisson random variable with parameter λ, compute E[1/(X + 1)]
4.20. How can I show that X is a Poisson random variable with parameter lambda, then E[Xn] =.... ? And after, using this result to compute E[X3]?
Let X be a Poisson random variable with E(X) = 3. Find P(2 < x < 4).
If the moment generating function of a random variable X is: (1/3+(2/3)e t ) 5 find P (X > 3).

SEE MORE QUESTIONS

Recommended textbooks for you

A First Course in Probability (10th Edition)

Probability

ISBN:

9780134753119

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability

Probability

ISBN:

9780321794772

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability (10th Edition)

Probability

ISBN:

9780134753119

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability

Probability

ISBN:

9780321794772

Author:

Sheldon Ross

Publisher:

PEARSON

SEE MORE TEXTBOOKS

roblem 3. Suppose that X and Y are independent Poisson random variables with param- ers λ and µ, respectively. Find the distribution of X + Y. Prove that the conditional stribution of X, given that X+Y = n, is binomial with parameters n and λ/(\+µ). (For 1 1:1 71 7 67 1m