Question 1. The joint distribution of X and Y is given. Are X and Y independent?...
The joint distribution of X and Y is given by x/y 1 3 1 0.06 0.42 0.12 2 0.04 0.28 0.08 1. Are X and Y independent or dependent? 2. Prove your answer in part 1.
The joint distribution of X and Y is given by |x/y 1 2 3 1 0.06 0.42 0.12 2 0.04 0.28 0.08 1. Are X and Y independent or dependent? 2. Prove your answer in part 1.
Question 4: Let X and Y be two discrete random variables with the following joint probability distribution (mass) function Pxy(x, y): a) Complete the following probability table: Y 2 f(x)=P(X=x) 1 3 4 0 0 0.08 0.06 0.05 0.02 0.07 0.08 0.06 0.12 0.05 0.03 0.06 0.05 0.04 0.03 0.01 0.02 0.03 0.04 2 3 foy)=P(Y=y) 0.03 b) What is P(X s 2 and YS 3)? c) Find the marginal probability distribution (mass) function of X; [f(x)]. d) Find the...
4. (20 points) Suppose the joint distribution of X and Y is: fxy(x, y) 1 0 1 2 3 0.04 0.06 0.01 0.00 0.13 0.13 0.02 0.12 0.04 0.06 0.00 0.11 0.07 0.10 0.06 (a) (4 points) Find the marginal distributions of X and Y. (b) (4 points) Given X = 3, what is the probability that random variable Y is at most 2?. (c) (4 points) Are random variables X and Y independent? Why or why not? (d) (4...
9. Let X and Y be Bernouilli random variables with joint distribution: Pr(X = 1 and Y = 1) = 0.42, Pr(X = 1 and Y = 0) = 0.18, Pr(X = 0 and Y = 1) = 0.28, Pr(X = 0 and Y = 0) = 0.12 Determine whether or not X and Y are independent. Determine the covariance and correlation for X and Y. Can you infer anything from this correlation?
0〈z,0〈y Given the following joint distributionfrY(x,y)-, cez+2y else Calculate the following 1. The value of c that makesfxy a proper pdf 2. The marginal distribution function fx(z) 3. The marginal distribution function fy () 4. P(X 1) 7. The random variables X and Y are independent if it is possible to write fxy (x, y) as the product of Íx (x) and fy (y) such that/xy(z, y) = k . Íx (x) . fy(y) for some value of k. Are...
2. Let X and Y be two continuous random variables varying in accordance with the joint density function, fx.y(z, y-e(x + y) for 0 < z < y < 1. Solve the following problem s. (1) Find e, fx(a) and fy (v) (2) Find fx-u(z) and fY1Xux(y) (8) Find P(Y e (1/2, 1)|X -1/3) and P(Y e (1/2,2)| X 1/3). 3. Find P(X < 2Y) if fx.y(zw) = x + U for X and Y each defined over the unit...
Question 4 Consider the following joint distribution of returns in Oil and Mining investments (as described in class slides for Chapter 4): Oil returns 10 5 0 -20 Mining returns marginal 0.20 0.16 0.10 0.02 0.48 0.08 0.26 0.12 0.06 0.52 marginal 0.28 0.42 0.22 0.08 1.00 where the entries in the central part of the matrice are the joint densities or frequencies. • Verify that Oil returns and Mining returns are not independent. • What is Pr(Oil return =...
Given the following joint distribution of two random variables X and Y (a) Compute marginal distribution PX(x) (b) Compute marginal distribution PY(y) (c) What is the conditional probability P(Y | X = 2)? 20.10 0.05 0.15 0.10 0.10 4 0.04 0.02 0.06 0.04 0.04 6 0.04 0.02 0.06 0.06 0.02 8 0.02 0.01 0.03 0 0.04
1) (15 pts) Random variables X and Y have joint PDF: 16e (2x+3) x20, y 20 fx.y(x, y) = 0 otw a.) (4 pts) What is P[X>Y]? b.) (6 pts) What are fx(x) and fy(y)? c.) (2 pts) Are X and Y independent? d.) (3 pts) What is P[max(X,Y) < 1)?