4.4-4. Let f(x, y) = 3/2, x² s ys 1, 0 < x s 1, be the joint pdf of X and Y. (a) Find P(0 < X < 1/2). (b) Find P(1/2

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Chapter1: Combinatorial Analysis
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4.4-4

0SKs1,0 sYs1.
(d) Find P(X SY).
4.4-2. Let X and Y have the joint pdf f(x. y) = x+ y.
(a) Find the marginal pdfs fy (x) and fy(y) and show that
f(x, y) # fx(x)fy(v). Thus, X and Y are dependent.
(b) Compute (i) µx, (ii) µy, (iii) o?, and (iv) .
4.4-3. Let f(x, y) = 2e¬*-y, 0 < x < y < 0o, be the joint
pdf of X and Y. Find fy(x) and fy (y), the marginal pdfs of
X and Y, respectively. Are X and Y independent?
4.4-4. Let f(x, y) = 3/2, x² < ys 1, 0 s x s 1, be the
joint pdf of X and Y.
(a) Find P(0 < X < 1/2).
(b) Find P(1/2 <Y < 1).
(c) Find P(X 2 1/2, Y > 1/2).
Transcribed Image Text:0SKs1,0 sYs1. (d) Find P(X SY). 4.4-2. Let X and Y have the joint pdf f(x. y) = x+ y. (a) Find the marginal pdfs fy (x) and fy(y) and show that f(x, y) # fx(x)fy(v). Thus, X and Y are dependent. (b) Compute (i) µx, (ii) µy, (iii) o?, and (iv) . 4.4-3. Let f(x, y) = 2e¬*-y, 0 < x < y < 0o, be the joint pdf of X and Y. Find fy(x) and fy (y), the marginal pdfs of X and Y, respectively. Are X and Y independent? 4.4-4. Let f(x, y) = 3/2, x² < ys 1, 0 s x s 1, be the joint pdf of X and Y. (a) Find P(0 < X < 1/2). (b) Find P(1/2 <Y < 1). (c) Find P(X 2 1/2, Y > 1/2).
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