Random variables X and Y have following distributions. PIX = -1) = 3/4, PIX = -2)...
Random variables X and Y have following distributions. PIX = -1) = 3/4, P(X = -2) - 1/4 PLY = 3) = 1/2, PIY = 2) = 1/2 a) Using the moment generating functions for random variables above find: E[X+Y] b) Using the moment generating functions for random variables above find: Var(X+Y)
Random variables X and Y have following distributions: PIX = -1) = 2/3, PIX = 2) = 1/3 PIY = -2) = 1/2, PſY = 3) = 1/2 a) (5 points) Using the moment generating functions for the random variables above find: E[X+Y] b) (5 points) Using the moment generating functions for the random variables above find: Var(X+Y)
Random variables X and Y have following distributions: PIX = -4) = 2/3, P(X = -1) = 1/3 PſY = 2) = 1/2, P(Y = 3) = 1/2 a) (5 points) Using the moment generating functions for the random variables above find: E[X+Y] b) (5 points) Using the moment generating functions for the random variables above find: Var(X+Y)
Random variables X and Y have following distributions. P(X = -1) = 3/4, P(X = 3) = 1/4 P(Y = -3) = 1/2, P(Y = 2) = 1/2 a) Using the moment generating functions for random variables above find: E[X+Y) b) Using the moment generating functions for random variables above find: Var(X+Y)
3. (4 points) The random variables X and Y are independent and have moment generating functions Find Var(X).x (t) =er-2t and Mr(t)=e3t2+tid t a) Find MGF of Z Find Var(Z). Find joint MGF of X and Z, i.e. Mxz(t1,t2) 2X-Y c) d)
Let X, Y be independent random variables where X is binomial(n = 4, p = 1/3) and Y is binomial(n = 3,p = 1/3). Find the moment-generating functions of the three random variables X, Y and X + Y . (You may look up the first two. The third follows from the first two and the behavior of moment-generating functions.) Now use the moment-generating function of X + Y to find the distribution of X + Y .
Let the random variable Y have the following probability distribution y 2 4 6 P(Y=y) 4/k 1/k 5/k find the value of k. find the moment-generating function of Y find Var(Y) using the moment generating function let W= 2Y-Y^2 +e^2*Y+7. find E(W)
X and Y are random variables (a) Show that E(X)=E(B(X|Y)). (b) If P((X x, Y ) P((X x})P({Y y)) then show that E(XY) = E(X)E(Y), i.e. if two random variables are independent, then show that they are uncorrelated. Is the reverse true? Prove or disprove (c) The moment generating function of a random variable Z is defined as ΨΖφ : Eez) Now if X and Y are independent random variables then show that Also, if ΨΧ(t)-(λ- (d) Show the conditional...
you have two random variables, X and Y with joint distribution given by the following table: Y=0 | .4 .2 4+.26. So, for example, the probability that Y 0, X - 0 is 4, and the probability that Y (a) Find the marginal distributions (pmfs) of X and Y, denoted f(x),f(r). (b) Find the conditional distribution (pmf) of Y give X, denoted f(Y|X). (c) Find the expected values of X and Y, E(X), E(Y). (d) Find the variances of X...
Practice problems using various statistical methods
If n independent random variables X have normal distributions with means μ and the standard deviations σ , then determine the distribution of a. I. X-E(X) var(X) C. 2. If n independent random variables Xi have normal distributions with means μί and the standard deviations σί, then determine the distribution of a. b. Y -a1X1 + a2X2+ + anXn (ai constant) X-E(X) Vvar(X) 3. What is CLT? Proof briefly? What are t-, Chi-squared- and...