Assume Xl and X2 are the endurance times (in days) ot two white rodents that were exposed to

various levels ot radiation. Expect to be that Xl and '(2 are free,

X, PAR(I. 1) and PARO.2)

(a) Give the joint pdt ot Xl and

(b) Find the likelihood that the subsequent rodent outlasts the main rodent, P[XI <

38..

Consider a couple ot ceaseless irregular factors X and Y witn a joint CDF ot the torm

what's more, zero in any case. Discover each ot the accompanying:

(a) The joint pot, f(x, y).

()Ptxso.5, YSO.51.

(d) hatchet + Y g 0.5].

(f)PIX+ 0<2.

39..

Leave X and Y alone nonstop arbitrary factors witn a joint pdt of the torm

furthermore, zero in any case.

(a) Find k so that t(x, y) is a joint pct.

(b) Find the marginals, tl(x) and f2(y).

(c) Fit-ld tne joint CDF, hatchet, Y).

(d) Find the restrictive pdt I x).

(e) Find the restrictive pdt I y).

40..

LetX1, X2, _ , X signify an arbitrary example trom a populace witn pdtt(x) - 3x2; x < 1, and

zero otnemise.

(a) Write down the joint pdtotX1, X2, Xn.

(b) Find the proabilhy that the primary perception is under 0.5, P[XI < 0.5].

(c) Find the proabilhy that all ot the perceptions are under 0.5.