Problem #1: Let X be a Poisson random variable with parameter 3, and Y a geometric random variable with parameter 1½ 3.Suppose that X and Y are independent, and W = X + Y . Find P{WX+Y. = 3}.Problem #1:Round your answer to 4 decimals.

Answered: Image /qna-images/answer/b7ff4785-d2a1-4049-97e9-50ed104749e3.jpg

Answered: Problem #1: Let X be a Poisson random…

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

Suppose that X, Y, and Z are jointly distributed random variables, that is, they are defined on the same sample space. Suppose that we also have the following. E(X)=0 Var(X) = 39 Var(Y) = 19 Var(Z) =24 E(Y) =-4 E(Z)=6 Compute the values of the expressions below. E(1+5z) = -Y-4Z E 2 Var(4–3Y) = I E(sz²) = I
Suppose that X, Y, and Z are jointly distributed random variables, that is, they are defined on the same sample space. Suppose that we also have the following. E(Y)=-7 Var (X) = 20 Var (Y)=6 Var (z) = 23 E (X) = 5 E(Z) = 3 Compute the values of the expressions below. E (-2X – 4) = -3Z + 2X E 3 Var (27 + 3) - O =(-sx") - O
7) Suppose that X and Y are two independent measurements. We can treat these measurements as random variables, where X has the mean of 1 and standard deviation of 2, and Y has the mean of 2 and the standard deviation of 3. For the transformations below, find the mean, variance, and the standard deviation. a) X+Y b) X-Y c) 2X+Y d) X-2Y+1
Question 3. Let X₁,, Xn be a random sample from a distribution with the pdf given by f₁₁x(x) = exp(-ª) if x ≥ A, otherwise f(x) = 0, where > 0. Find the MLE's of 0 and X. Start by writing the likelihood function and note the constraint involving A. Question 4. #4.2.9 of the textbook.
(a) Recall that for a random variable X and constants a and b, E(aX+b) = aE(X) +b. Prove that Var(aX + b) = = a²Var(X). (b) Mike agrees to donate 50 dollars to charity, plus 25 dollars for every goal scored in a particular World Cup soccer game. Thus Mike's donation is a random variable Y = 25X + 50 where X is defined in problem 1. Find the expected value and the variance of Y.
Problem #2: If two loads are applied to a cantilever beam as shown in the figure below, the bending moment at 0 due to the loads is a1X₁ + a₂X₂. Problem =2(a) Problem =2(b) X1 Problem #2(c): a X₂ 9 Suppose that X₁ and X2 are independent random variables with means 2 and 5 kips, respectively, and standard deviations 0.7 and 1.5 kips. respectively. Suppose that a₁ = 3 ft and a2 = 10 ft. (a) Find the expected value of the bending moment. (b) Find the standard deviation of the bending moment. (c) If X₁ and X₂ are normally distributed, what is the probability that the bending moment will exceed 82 kip-ft? answer correct to 4 decimals answer correct to 4 decimals

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

Problem #1: Let X be a Poisson random variable with parameter 3, and Y a geometric random variable with parameter 1½ 3. Suppose that X and Y are independent, and W = X + Y . Find P{W X+Y. = 3}. Problem #1: Round your answer to 4 decimals.