Question

10. The proportional gain in weight by a newborn puppy in its first 2 weeks of life is given by a random variable W where fw(w) = {30, otherwise 3w2,0 <w<1 0, otherwise a) (6 pts.) Find the probability that W is more than 0.5. - b) (6 pts. Find the CDF of W. c) (10 pts. Find the mean and variance of W.

Answer 1

30² the (W) oswsi otherwise if tw (W) dws f 3w2dw 0.5 3 u 0.5 1-0.53 0.875 IP (W) 0.5) for w co 0 = ( د ) ع for wel Flo) tuldn. OS 11 3 x2 og 23 for w > 1 f(W) = 1 w.co Fw (W) = ws Oc wsi w71 1

Elw) = I'wt W tlw) dw f3w3 3 w3 dow wt 3 3 E(W) mit 0.75 ELW?) 3 wt aw - 3 3 alls vare (W) = E(W2) -(E (W)? 3 9 vare (W) 0.0375