Let X and Y be independent random variables. Random variable X has a discrete uniform distribution...
Let X and Y be independent random variables. Random variable X
has a discrete
uniform distribution over the set {1, 3} and Y has a discrete
uniform distribution over
the set {1, 2, 3}. Let V = X + Y and W = X − Y .
(a) Find the PMFs for V and W.
(b) Find mV and
(c) Find E[V |W >0].
Homework Answers
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Let X and Y be independent random variables. Random variable X
has a discrete
uniform distribution...
2. Let X and Y be two independent discrete random variables with the probability mass functions...
2. Let X and Y be two independent discrete random variables with the probability mass functions PX- = i) = (e-1)e-i and P(Y = j-11' for i,j = 1, 2, Let {Uni2 1} of i.i.d. uniform random variables on [0, 1]. Assume the sequence {U i independent of X and Y. Define M-max(UhUn Ud. Find the distribution
3. (Bpoints) Let X, Y and Z be independent uniform random variables on the interval (0, 2), Let W...
3. (Bpoints) Let X, Y and Z be independent uniform random variables on the interval (0, 2), Let W min(X, y.z a) Find pdf of W Find E(1-11 b)
3. (Bpoints) Let X, Y and Z be independent uniform random variables on the interval (0, 2), Let W min(X, y.z a) Find pdf of W Find E(1-11 b)
12. Let X and Y be independent random variables, where X has a uniform distribution on...
12. Let X and Y be independent random variables, where X has a uniform distribution on the interval (0,1/2), and Y has an exponential distribution with parameter = 1. (Remember to justify all of your answers.) (a) What is the joint distribution of X and Y? (b) What is P{(x > 0.25) U (Y > 0.25)}? (c) What is the conditional distribution of X. given that Y - 3? (d) What is Var(Y - E[2X] + 3)? (e) What is...
Q6 (4pt) Let X be a discrete uniform random variable over {1,2,...,6} and let Y be...
Q6 (4pt) Let X be a discrete uniform random variable over {1,2,...,6} and let Y be a Bernoulli random variable with parameter 1/2 such that X, Y are independent. (1) Find the PMF of the random variable Z, where Z XY. (2) Compute the third moment of Z, that is, E[z2
Proposition 6.10 Independent Discrete Random Variables: Bivariate Case Let X andY be two discrete...
Proposition 6.10 Independent Discrete Random Variables: Bivariate Case Let X andY be two discrete random variables defined on the same sample space. Then X and Y are independent if and only if pxy(x,y) = px(x)py(y), for all x , y ER. (6.19) In words, two discrete random variables are independent if and only if their joint equals the product of their marginal PMFs. Proposition 6.11 Independence and Conditional Distributions Discrete random variables X and Y are independent if and only...
3Y 2 1. (20 points) Suppose that X and Y independent random variables. Let W 2x (a) Consider the following probability...
3Y 2 1. (20 points) Suppose that X and Y independent random variables. Let W 2x (a) Consider the following probability distribution of a discrete random variable X: 12 P(X) 00.7 0.3 X Compute the mean and variance of X (b) Use your answers in part (a). If E(Y)=-3 and V(Y)= 1, what are E(W) and V (W)?
Let X be a uniform(0, 1) random variable and let Y be uniform(1,2) with X and...
Let X be a uniform(0, 1) random variable and let Y be uniform(1,2) with X and Y being independent. Let U = X/Y and V = X. (a) Find the joint distribution of U and V . (b) Find the marginal distributions of U.
12. Let X and Y be independent random variables, where X has a uniform distribution on the interval (0,1/2), and Y...
12. Let X and Y be independent random variables, where X has a uniform distribution on the interval (0,1/2), and Y has an exponential distribution with parameter A= 1. (Remember to justify all of your answers.) (a) What is the joint distribution of X and Y? (b) What is P{(X > 0.25) U (Y> 0.25)}? nd (c) What is the conditional distribution of X, given that Y =3? ur worl mple with oumbers vour nal to complet the ovaluato all...
4- Let Y = X, where X is a discrete uniform integer random variable in the...
4- Let Y = X, where X is a discrete uniform integer random variable in the range [-4,4). a) What is the PMF of the variable X? b) What is the PMF of the variable Y? c) Draw the PMF of the variables X, and Y. d) Draw the CDF of the variables X, and Y. e) What is the expected value of the random variables X and Y? f) What is the variance of the random variables X and...
Let X and Y be two discrete random independent random variables. p(x) = 1/3 for x...
Let X and Y be two discrete random independent random variables. p(x) = 1/3 for x =-2,-1,0 p(y) = 1/2 for y =1,6 Z = X + Y. What is the distribution of Z using the method of MGF's
2. Let X and Y be two independent discrete random variables with the probability mass functions PX- = i) = (e-1)e-i and P(Y = j-11' for i,j = 1, 2, Let {Uni2 1} of i.i.d. uniform random variables on [0, 1]. Assume the sequence {U i independent of X and Y. Define M-max(UhUn Ud. Find the distribution
3. (Bpoints) Let X, Y and Z be independent uniform random variables on the interval (0, 2), Let W min(X, y.z a) Find pdf of W Find E(1-11 b)
3. (Bpoints) Let X, Y and Z be independent uniform random variables on the interval (0, 2), Let W min(X, y.z a) Find pdf of W Find E(1-11 b)
12. Let X and Y be independent random variables, where X has a uniform distribution on the interval (0,1/2), and Y has an exponential distribution with parameter = 1. (Remember to justify all of your answers.) (a) What is the joint distribution of X and Y? (b) What is P{(x > 0.25) U (Y > 0.25)}? (c) What is the conditional distribution of X. given that Y - 3? (d) What is Var(Y - E[2X] + 3)? (e) What is...
Q6 (4pt) Let X be a discrete uniform random variable over {1,2,...,6} and let Y be a Bernoulli random variable with parameter 1/2 such that X, Y are independent. (1) Find the PMF of the random variable Z, where Z XY. (2) Compute the third moment of Z, that is, E[z2
Proposition 6.10 Independent Discrete Random Variables: Bivariate Case Let X andY be two discrete random variables defined on the same sample space. Then X and Y are independent if and only if pxy(x,y) = px(x)py(y), for all x , y ER. (6.19) In words, two discrete random variables are independent if and only if their joint equals the product of their marginal PMFs. Proposition 6.11 Independence and Conditional Distributions Discrete random variables X and Y are independent if and only...
3Y 2 1. (20 points) Suppose that X and Y independent random variables. Let W 2x (a) Consider the following probability distribution of a discrete random variable X: 12 P(X) 00.7 0.3 X Compute the mean and variance of X (b) Use your answers in part (a). If E(Y)=-3 and V(Y)= 1, what are E(W) and V (W)?
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