Please give your previous question ... then definitely I will give a good answer...
3. For X and Y from the previous question, find a) PCX > 11Y S 1.5)...
Question 12: Let X and Y have the joint probability density function Find P(X>Y), P(X Y <1), and P(X < 0.5)
Let X, Y ~ 10,11 independently. Find P(max(X, Y} > 0.8 1 min(X, Y} = 0.5)
Let X, Y be two independent exponential random variables with means 1 and 3, respectively. Find P(X> Y)
Prove that there are no natural number solutions to the equation where x, y ≥ 2 ... (See Picture Below) Prove that there are no natural number solutions to the equation where X, Y > 2. x2 - y2 = 1.
For f(x, y) = k(x2 + y2), 0<x< 1 and 0 <y<1 and 0 elsewhere: a) Find k. b) Are X and Y independent? c) Find P(X<0.5, Y>0.5), P( X = 0.5, Y>0.5).
8. Find the marginal-product functions for the Cobb-Douglas production func- tion y = A.X. XXX A>0,0<«; <1 for i = 1, 2, 3, 4
Let the joint pmf of X and Y be p(x, у) схуг, x-1,2,3, y-12. a) Find constant c that makes p(x, y) a valid joint pmf. c) Are X and Y independent? Justify d) Find P(X+Y> 3) and PCIX-YI # 1)
Exercise 4.9. Let X ~ Poisson(10). (a) Find P(X>7). (b) Find P(X < 13 X > 7).
7. Suppose X and Y have joint pdf f(x,y) = 24x y if x >0, y>0,x+y<1 and 0 otherwise. Find P(Y > 2x).
The joint pdf of X and Y is f(x, y) = x for x > 0, y > 0, x + y < 2. (a) Find P(Y > 2X). (b) Find E(XY). (c) Find P(0.7 < X < 1.71Y = 0.5).