Question

5.1.8 Determine the value of c that makes the function f(x, y) = c(x + y) a joint probability density function over the range 0 < x < 3 and x < y < x + 2. c = (give the exact answer in the form of fraction) Determine the following. Round your answers in a-f to four decimal places.

a. P(X < 1, Y < 2) =

b. P(1 < X < 2) =

c. P(Y > 1) =

d. P(X < 2, Y < 2) =

e. E(X) =

f. V(X) =

g. Marginal probability distribution of X. fX(x) =

for ___ < x < _____

h. Conditional probability distribution of Y given that X = 1. fY|X(y) =

for ____ < y < ____

i. E(Y|X = 1) = (round the answer to four decimal places)

j. P(Y > 2|X = 1) = (round the answer to four decimal places)

k. Conditional probability distribution of X given that Y = 2. fX|Y=2(x) =

for ______ < x < _______

Answer 1