Reference no: EM13961213

Question 1) Let X denote the number of times a certain numerical control machine will malfunction: 0, 1, 2, or 3 times on a given day. Let Y denote the number of times a technician is called on an emergency call. Their joint probability mass distribution of X and Y is given by

P(x) = (x + y)/30

for x = 0, 1, 2, 3; and y = 0, 1, 2, find the following:

(a) P( X > 2, Y < 1)

(b) P( X > Y)

(c) P( X + Y = 3)

(d) Marginal of X.

(e) P( Y = 3 I X = 2)

Question  2) The joint density of X and Y is given by

f (x, y) = {(6-x-y)/8, 0 < x < 2, 2< y< 4
                  0,                  Otherwise
(a) Find P( X > 1)

(b) Find P( X > 1, Y < 3)

(c) Find P( X + Y < 3 ) 

Question 3) Two tire-quality experts examine stacks of tires and assign quality ratings to each tire on a 3-point scale. Let X denote the grade given by expert A and Y denote the grade given by B.

The following table gives the joint distribution for X and Y.

f(x,y)                 y

                 1       2       3

x    1        0.14   0.05   0.02

     2         0.10   0.35   0.05

     3         0.03   0.10   0.20

(a) Compute E(X)

(b) Compute E(Y)

(c) Compute E[h(X, Y)] where h[X, Y] = X + Y

(d) Compute Cov(X, Y)

(e) Compute Corr(X, Y)