Question

3-1.1 Two random variables have joint PDF of F(x, y) = 0 for x < 0 and y <0 xy for 0 ? x ? 1 and 0 ? y ? 1 1 for x > 1 and y >1 a) Find the joint and marginal pdfs. b) USE F(x, y) and find P(X < 3/4, Y> 1/4), P(X < 3/4, Y=1/4), P(X ? 1/4) 3-1.2 Let f(x, y) = kxy for 0 ? x ? 1 and 0? y ?1 and 0 elsewhere, a) Find k b) Find marginal pdfs. c) Are X and Y independent? d) Find P(X < 1/2, Y> 1/2).

          3-1.1 Two random variables have joint PDF of
F(x, y) = 0 for x < 0 and y <0
xy for 0 ? x ? 1 and 0 ? y ? 1
1 for x > 1 and y >1
a) Find the joint and marginal pdfs.
b) USE F(x, y) and find P(X < 3/4, Y> 1/4), P(X < 3/4, Y=1/4), P(X ? 1/4)
3-1.2 Let f(x, y) = kxy for 0 ? x ? 1 and 0? y ?1 and 0 elsewhere,
a) Find k
b) Find marginal pdfs.
c) Are X and Y independent?
d) Find P(X < 1/2, Y> 1/2).

3-1.1 Two random variables have joint PDF of
F(x, y) = 0 for x < 0 and y <0
xy for 0 ? x ? 1 and 0 ? y ? 1
1 for x > 1 and y >1
a) Find the joint and marginal pdfs.
b) USE F(x, y) and find P(X < 3/4, Y> 1/4), P(X < 3/4, Y=1/4), P(X ? 1/4)
3-1.2 Let f(x, y) = kxy for 0 ? x ? 1 and 0? y ?1 and 0 elsewhere,
a) Find k
b) Find marginal pdfs.
c) Are X and Y independent?
d) Find P(X < 1/2, Y> 1/2).

Added by Kelly S.

University Physics with Modern Physics

Hugh D. Young 14th Edition

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3-1.1 Two random variables have a joint PDF of fxy = 0 for x < 0 and y < 0, fxy = xy for 0 â‰¤ x â‰¤ 1 and 0 â‰¤ y â‰¤ 1, and fxy = 1 for x > 1 and y > 1. a) Find the joint and marginal PDFs. b) Use fxy and find P(X â‰¤ 3/4, Y > 1/4), P(X = 3/4, Y = 1/4), and P(X â‰¤ 1/4). 3-1.2 Let fxy = kxy for 0 â‰¤ x â‰¤ 1 and 0 â‰¤ y â‰¤ 1, and fxy = 0 elsewhere. a) Find k. b) Find the marginal PDFs. c) Are X and Y independent? d) Find P(X â‰¤ 1/2, Y > 1/2).