Probability Distribution Doubts

[Homer Simpson]

Q) If the joint probability density function of X and Y is given by

f(x,y) = 2 for     x>0, y>0, x+y<1
         = 0           elsewhere

find: - P(X+Y>2/3) -- Please explain what range to use for x, y in the integral -

Ans: 5/9

Q) Determine k so that

f(x,y) = kx(x-y)         for 0<x<1 , -x<y<x
          =  0                 elsewhere

can serve as probability distribution - getting confused about what to do with y!

Q) If Joint PDF of X and Y is given by -

f(x,y) = 24xy    for 0<x<1, 0<y<1, x+y<1
         = 0                elsewhere

Fine P(X+Y<1/2) - Am getting 1/16

Please confirm answer and correct me if i am wrong (about range)

Thanks a ton!

[Akshay Jain]

[Akshay Jain]

[Akshay Jain]

yes for 3rd 1/16 is coming

[Homer Simpson]

  Thank you! Got it now!