Question 6: (5 marks). Let (X, Y) have the joint probability function (2r y)/15, r=1,2,3;y 1,2;...
Let X and Y be two random variables with joint probability mass function: (?,?) = (??(3+?))/(18*3+30)??? ?=1,2,3 ??? ?=1,2 (?,?) = 0, Otherwise. Please enter the answer to 3 decimal places. Find P(X>Y) and Let X and Y be two random variables with joint probability mass function: (?,?) = (??(4+?))/(18*4+30)??? ?=1,2,3 ??? ?=1,2 (?,?) = 0, Otherwise. Please enter the answer to 3 decimal places. Find P(Y=2/X=1) Please show work/give explanation
We have the following joint PMF of X and Y: Pxy (x,y) ſa(x+3y) x =1,2,3; y =1,2 0 otherwise Find: 1. the value of a 2. the marginal PMFs of X and Y 3. if X and Y are independent
Question 1(a&b) Question 3 (a,b,c,d) QUESTION 1 (15 MARKS) Let X and Y be continuous random variables with joint probability density function 6e.de +3,, х, у z 0 otherwise f(x, y 0 Determine whether or not X and Y are independent. (9 marks) a) b) Find P(x> Y). Show how you get the limits for X and Y (6 marks) QUESTION 3 (19 MARKS) Let f(x, x.) = 2x, , o x, sk: O a) Find k xsl and f(x,...
5. Let X and Y have joint probability density function of the form Skxy if 0 < x +y < 1, x > 0 and y > 0, f(x,y)(, y) = { 0 otherwise. (a) What is the value of k? (b) Giving your reasons, state whether X and Y are dependent or independent. (c) Find the marginal probability density functions of X and Y. (d) Calculate E(X) and E(Y). (e) Calculate Cov(X,Y). (f) Find the conditional probability density function...
Let X and Y have the joint pmf defined by (х, у) (1,2) (0,0) (0,1) (0,2) (1,1) (2,2) 2/12 1/12 3/12 1/12 1/12 4/12 Pxy (x, y) Find py (x) and p, (y) а. b. Are X and Y independent? Support your answer. Find x,y,, and o, С. d. Find Px.Y
(1 point) 1. (Old Quiz Question) Let X and Y have the joint probability density function 1 for 01,0 y< 1 0 elsewhere (a) Calculate P(X-Y < 0.5) (b) Calculate PXY 0.25) (c) Find P(X 0.75|XY>0.25)
aercise 6.43. Let the random variables X, Y have joint density function 2r y + vy, ifo<r< 1 and 0< fx,y(x, y) 0, else. Let T = min(X, Y) and V max(X,Y). Assuming that T, V are jointly ontinuous, find their joint density function. Hint. Look at Example 6.40. aercise 6.43. Let the random variables X, Y have joint density function 2r y + vy, ifo
5. (a) (6 marks) Let X be a random variable following N(2.4). Let Y be a random variable following N(1.8). Assume X and Y are independent. Let W-min(x.Y). Find P(W 3) (b) (8 marks) The continuous random variables X and Y have the following joint probability density function: 4x 0, otherwise Find the joint probability density function of U and V where U-X+Y and -ky Also draw the support of the joint probability density function of Uand V (o (5...
Question 4: (5 Marks) Let X and Y be continuous random variables have a joint probability density function of the form: f(x,y) = cy2 + x 0 SX S1, 0 Sys1. Determine the following: 1. The value of c. 2. The marginal distributions f(x) and f(y). 3. The conditional distribution f(xly). 4. Are X and Y independent? Why? - the
5. Let the joint probability density function of X and Y be given by, f(x,y) = 0 otherwise (a) Find the value of A that makes f (x, y) a proper probability density function (b) Calculate the correlation coefficient of X and Y. (c) Are X and Y independent? Why or why not?