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Problem 2. Suppose a website sells X computers where X is modeled as a geometric random...
2. Det X be a geometric random variable with mean S. Define a new random variable Y using the following function Y-11,-31 ifXcS 2 ifX25 Where| | denote the absolute value. (a) Find the PMF ofY (b) Fi...
2. Det X be a geometric random variable with mean S. Define a new random variable Y using the following function Y-11,-31 ifXcS 2 ifX25 Where| | denote the absolute value. (a) Find the PMF ofY (b) Find the CDF of Y (c) Find E[Y] and Var(Y] (d) Find P IYel Y 3]
2. Det X be a geometric random variable with mean S. Define a new random variable Y using the following function Y-11,-31 ifXcS 2 ifX25 Where| |...
1. The proportion of defective items in a large lot is p. Suppose a random sample of n items is s...
1. The proportion of defective items in a large lot is p. Suppose a random sample of n items is selected from the lot. Let X denote the mumber of defective itens in the sample and let denote the number of non-defective items. (a) Specify the distributions of X and Y, respectively. Are they independent? (b) Find E(X-Y) and var(X Y).
1. The proportion of defective items in a large lot is p. Suppose a random sample of n items...
Problem 5 (10 points). Suppose that the independent Bernoulli trials each with success probability p, are...
Problem 5 (10 points). Suppose that the independent Bernoulli trials each with success probability p, are performed independently until the first success occurs, Let Y be the number of trials that are failure. (1) Find the possible values of Y and the probability mass function of Y. (2) Use the relationship between Y and the random variable with a geometric distribution with parameter p to find E(Y) and Var(Y).
1. Suppose X,Y are random variables whose joint pdf is given by f(x, y) = 1/...
1. Suppose X,Y are random variables whose joint pdf is given by f(x, y) = 1/ x , if 0 < x < 1, 0 < y < x f(x, y) =0, otherwise . Find the covariance of the random variables X and Y . 2.Let X1 be a Bernoulli random variable with parameter p1 and X2 be a Bernoulli random variable with parameter p2. Assume X1 and X2 are independent. What is the variance of the random variable Y...
4. (9 pts) Suppose the random variable Y has a geometric distribution with parameter p. Let...
4. (9 pts) Suppose the random variable Y has a geometric
distribution with parameter p. Let ?? = √?? 3 3 . Find the
probability distribution of V
3 4. (9 pts) Suppose the random variable Y has a geometric distribution with parameter p. Let V 3 Find the probability distribution of.
2. (Ross 3.2) Let Xi and X2 be independent geometric random variables having the same parameter...
2. (Ross 3.2) Let Xi and X2 be independent geometric random variables having the same parameter p. (a) Compute the pmf for the random variable Y (b) Compute Pr(X,-iX, +X2=n) - Xi+ X2
Suppose that a random variable X has the following pdf: 8px+2(1-P) 0<x<0.5., JxX;P) = *; where...
Suppose that a random variable X has the following pdf: 8px+2(1-P) 0<x<0.5., JxX;P) = *; where 0 Sp Si 0 otherwise where p is simply a constant that has yet to be specified in other words, p is a parameter). For now, we will leave the parameter p an unspecified constant ► Find P(X>0.3) = Note: your answer will be an expression containing p. Suppose that k> 0 is also a constant (not yet specified). Find the expected value of...
3. Let X be a discrete random variable with the following PMF: 0.1 for x 0.2...
3. Let X be a discrete random variable with the following PMF: 0.1 for x 0.2 for 0.2 for x=3 Pg(x)=〈 0.1 for x=4 0.25 for x=5 0.15 for x=6 otherwise a) (10 points) Find E[X] b) (10 points) Find Var(X) c) Let Y-* I. (15 points) Find E[Y] II. (15 points) Find Var(Y) X-HX 4. Consider a discrete random variable X with E [X]-4x and Var(X) = σ. Let Y a. (10 points) Find E[Y] b. (20 points) Find...
Problem D: Suppose X1, .,X, are independent random variables. Let Y be their sum, that is...
Problem D: Suppose X1, .,X, are independent random variables. Let Y be their sum, that is Y 1Xi Find/prove the mgf of Y and find E(Y), Var(Y), and P (8 Y 9) if a) X1,.,X4 are Poisson random variables with means 5, 1,4, and 2, respectively. b) [separately from part a)] X,., X4 are Geometric random variables with p 3/4. i=1
Please answer both. . Suppose that Y is a random variable with distribution function below. 1-e-v/2,...
Please answer both.
. Suppose that Y is a random variable with distribution function below. 1-e-v/2, 0, y > 0; otherwise F(y) = (a) Find the probability density function (pdf) f(y) of Y. yso (b) E(Y) and Var(Y) 5. Suppose X is a random variable with E(X) 5 and Var(X)-2. What is E(X)?
2. Det X be a geometric random variable with mean S. Define a new random variable Y using the following function Y-11,-31 ifXcS 2 ifX25 Where| | denote the absolute value. (a) Find the PMF ofY (b) Find the CDF of Y (c) Find E[Y] and Var(Y] (d) Find P IYel Y 3]
2. Det X be a geometric random variable with mean S. Define a new random variable Y using the following function Y-11,-31 ifXcS 2 ifX25 Where| |...
1. The proportion of defective items in a large lot is p. Suppose a random sample of n items is selected from the lot. Let X denote the mumber of defective itens in the sample and let denote the number of non-defective items. (a) Specify the distributions of X and Y, respectively. Are they independent? (b) Find E(X-Y) and var(X Y).
1. The proportion of defective items in a large lot is p. Suppose a random sample of n items...
Problem 5 (10 points). Suppose that the independent Bernoulli trials each with success probability p, are performed independently until the first success occurs, Let Y be the number of trials that are failure. (1) Find the possible values of Y and the probability mass function of Y. (2) Use the relationship between Y and the random variable with a geometric distribution with parameter p to find E(Y) and Var(Y).
4. (9 pts) Suppose the random variable Y has a geometric
distribution with parameter p. Let ?? = √?? 3 3 . Find the
probability distribution of V
3 4. (9 pts) Suppose the random variable Y has a geometric distribution with parameter p. Let V 3 Find the probability distribution of.
2. (Ross 3.2) Let Xi and X2 be independent geometric random variables having the same parameter p. (a) Compute the pmf for the random variable Y (b) Compute Pr(X,-iX, +X2=n) - Xi+ X2
Suppose that a random variable X has the following pdf: 8px+2(1-P) 0<x<0.5., JxX;P) = *; where 0 Sp Si 0 otherwise where p is simply a constant that has yet to be specified in other words, p is a parameter). For now, we will leave the parameter p an unspecified constant ► Find P(X>0.3) = Note: your answer will be an expression containing p. Suppose that k> 0 is also a constant (not yet specified). Find the expected value of...
3. Let X be a discrete random variable with the following PMF: 0.1 for x 0.2 for 0.2 for x=3 Pg(x)=〈 0.1 for x=4 0.25 for x=5 0.15 for x=6 otherwise a) (10 points) Find E[X] b) (10 points) Find Var(X) c) Let Y-* I. (15 points) Find E[Y] II. (15 points) Find Var(Y) X-HX 4. Consider a discrete random variable X with E [X]-4x and Var(X) = σ. Let Y a. (10 points) Find E[Y] b. (20 points) Find...
Problem D: Suppose X1, .,X, are independent random variables. Let Y be their sum, that is Y 1Xi Find/prove the mgf of Y and find E(Y), Var(Y), and P (8 Y 9) if a) X1,.,X4 are Poisson random variables with means 5, 1,4, and 2, respectively. b) [separately from part a)] X,., X4 are Geometric random variables with p 3/4. i=1
Please answer both.
. Suppose that Y is a random variable with distribution function below. 1-e-v/2, 0, y > 0; otherwise F(y) = (a) Find the probability density function (pdf) f(y) of Y. yso (b) E(Y) and Var(Y) 5. Suppose X is a random variable with E(X) 5 and Var(X)-2. What is E(X)?
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