LetXandYbecontinuousrandomvariableshavingthejointpdff(x,y)=8xy;0≤y≤x≤1.(a)SketchthegraphofthesupportofXandY.(b)Findf1(x),themarginalpdfofX.(c)Findf2(y),themarginalpdfofY.(d)ComputemeanofX,meanof

Question

Let X and Y be continuous random variables having the joint pdf f(x,y) = 8xy; 0 ≤ y ≤x ≤ 1.
(a) Sketch the graph of the support of X and Y .
(b) Find f1(x),the marginal pdf of X.
(c) Find f2(y),the marginal pdf of Y .
(d) Compute mean of X,mean of Y ,variance of X,variance of Y,Cov(X,Y ),and ρ.
(e) Find g(x|y=1/2),the conditional pdf of X given Y = 1/2.
(f) Find P(X < 3/4 | Y=1/2).
(g) Find P(X< 3/4 | Y

Answer 1

a）画出 y ≤x ;0 ≤ y ≤ 1 ;0 ≤x ≤ 1.区域
b）f1(x),=8y
c）f2(y),=8x
d）不知道
e）g(x|y=1/2)=4
能力有限啊