please asap 3. The table to the right shows the values of the joint probability distribution of the discrete random variables X and Y Find the cov(X, Y). ơxy- 11-u,' y. 0 0 1/12 1/6 1/24 7/2...
The discrete random variables X and Y take integer values with joint probability distribution given by f (x,y) = a(y−x+1) 0 ≤ x ≤ y ≤ 2 or =0 otherwise, where a is a constant. 1 Tabulate the distribution and show that a = 0.1. 2 Find the marginal distributions of X and Y. 3 Calculate Cov(X,Y). 4 State, giving a reason, whether X and Y are independent. 5 Calculate E(Y|X = 1).
3. Let X and Y have a discrete joint distribution with Table 1: Joint discrete distribution of X and Y Values of Y -1 0 1 Values of X -1 1 į 0 1 1 0 -600-100 Then, find the following: • the marginal distribution of X; [2 points) • the marginal distribution of Y; [2 points] the conditional distribution of X given Y = -1; [2 points] Are X and Y are independent? Discuss with proper justification. (3 points)...
If the joint probability distribution of three discrete random variables X, Y , and Z is given by: f(x, y, z) = (x + y)z / 63 , for x = 1, 2; y = 1, 2, 3; z = 1, 2. Find the probability P(X = 2, Y + Z ≤ 3)
3. Suppose X, Y are discrete random variables taking values in {-1,0,1) and their joint probability mass function is 0 X=1 where a, b are two positive real numbers. (i) Find the values of a and b such that X and Y are uncorrelated. (ii) Show that X and Y cannot be independent 0
3. Suppose X, Y are discrete random variables taking values in -1,0,1) and their joint probability mass function is 0 0 0 where a, b are two positive real numbers. (i) Find the values of a and b such that X and Y are uncorrelated (ii) Show that X and Y cannot be independent
2. Let X and Y be two random variables with a joint distribution (discrete or continuous). Prove that Cov(X,Y)= E(XY) - E(X)E(Y). (15 points) 3. Explain in detail how we can derive the formula Var(X) = E(X) - * from the formula in Problem 2 above. (Please do not use any other method of proof.) (10 points)
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...
The table below shows the probability distribution of a discrete random variable X. Values of the random variable X (x) Probability of observing each value of X P(X = x) 6 0.20 7 0.25 8 0.25 9 0.10 10 0.12 11 0.08 Total 1.00 (a) Determine the probability that the random variable X is between 8 and 10, inclusive. (1 mark (b) Determine the probability that the random variable X is at least 9. (1 mark) c. Determine the probability...
3. Let the random variables X and Y have the joint probability density function 0 y 1, 0 x < y fxy(x, y)y otherwise (a) Compute the joint expectation E(XY) (b) Compute the marginal expectations E(X) and E (Y) (c) Compute the covariance Cov(X, Y)
Let X and Y be discrete random variables with the joint probability function f(x,y) given by the table: х f(x,y) 7 9 11 20.050.15 0.1 Y 30.15 0.40.15 Which of the following is the conditional probability function fxy (x|3) ? X = x 7 9 11 fxry(x3)0.28|0.37.42 X = X 7 9 11 fxıy(x3)0.30.280.42 X = x 9 7 11 fxıy(x|3)|0.2143|0.2143|0.5714 X = X 7 11 fxxy(xl3)|0.21430.57140.2143 ОО None of the above