Question about Probability density function
Let X and Y have joint probability density function f(x,y) (s,t) = ce ^ -(s + 2t) for 0 <= s, and 0 <= t. Find
(a) c
(b) Pr {min (X, Y) 1/3}
(c) Pr {X <= Y}
(d) The marginal probability density function of X
(e) E [XY]
Let X and Y be independent uniform (0,1) random variables. Compute
(a) Pr {X < Y}
(b) Pr {X = Y}
(c) The probability density function of X + Y
(d) Var[X]
(e) Var[X + Y]