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).
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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