Consider the following densit y function: f(x) = kx for 0 < x < 4 ; 0 - Otherwise

a) Evaluate k,
b) Find F(x)
c) E valuate P ( X < 1 ) , P (1 < X < 3), and P ( X > 3)

5. Suppose that X and Y has the following joint probability distribution: x f (x, y) 2 4 1 0.2 0.15 y 3 0.1 0.15 5 0.1 0.3

a) Find the M arginal distribution of X: g(x) => g(2) and g(4)
b) Find Marginal distribution of Y: h(y) => h(1), h(3), and h(5)
c) What is the value of f(2,1), f(4,3) and f( 4,5 )
d ) Find P ( Y = 3 | X = 4), P ( X = 2 | Y = 3), and P ( Y = 5 | X = 2)
e) Determine whether two random variables X and Y are dependent or independent? Annotations