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The joint probability distribution of X and Y is given by f(x) = { c(x +...

The joint probability distribution of X and Y is given by f(x) = { c(x + y) x = 0, 1, 2, 3; y = 0, 1, 2. 0 otherwise

(1) Find the value of c that makes f(x, y) a valid joint probability density function.

(2) Find P(X > 2; Y < 1).

(3) Find P(X + Y = 4).

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Answer #1

Answer:

Given that:

f(x,y) = c(x+y)

f(x,y) y=0 y=1 y=2
x=0 0 c 2c
x=1 c 2c 3c
x=2 2c 3c 4c
x=3 3c 4c 5c

(1) Find the value of c that makes f(x, y) a valid joint probability density function.

Total probability = 1

(2) Find P(X > 2; Y < 1).

(3) Find P(X + Y = 4).

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