# Question: The joint probability density function of X and Y is

The joint probability density function of X and Y is given by

f (x, y) = 6/7(x2 + xy/2) 0 < x < 1, 0 < y < 2

(a) Compute the density function of X.

(b) Find P{X > Y}.

(c) Find P{Y > 1/2|X < 1/2}.

f (x, y) = 6/7(x2 + xy/2) 0 < x < 1, 0 < y < 2

(a) Compute the density function of X.

(b) Find P{X > Y}.

(c) Find P{Y > 1/2|X < 1/2}.

## Answer to relevant Questions

Verify Equation (1.2). Consider a sequence of independent trials, with each trial being a success with probability p. Given that the kth success occurs on trial n, show that all possible outcomes of the first n − 1 trials that consist of k − 1 ...Suppose that W, the amount of moisture in the air on a given day, is a gamma random variable with parameters (t, β). That is, its density is f(w) = βe−βw(βw)t−1 / Γ(t), w > 0. Suppose also that given that W = w, the ...Suggest a procedure for using Buffon’s needle problem to estimate π. Surprisingly enough, this was once a common method of evaluating π. Consider n independent flips of a coin having probability p of landing on heads. Say that a changeover occurs whenever an outcome differs from the one preceding it. For instance, if n = 5 and the outcome is HHTHT, then there ...Post your question