Question

Hi! Please help me on this question #41.

Thank you so much!

(by giving the p.m.f. or p.d.f.) whose the cumulative distribution function F(t) satisfies F(n) = 1 - 1 for each positive integer n. Exercise 3.41. We produce a random real number X through the following two- stage experiment. First roll a fair die to get an outcome Y in the set {1,2,...,6}. Then, if Y = k, choose X uniformly from the interval (0, k]. Find the cumulative distribution function F(s) and the probability density function f(s) of X for 3 < s<4.

Answer 1

Solution : Given Data Exercise 3.41: we Product the through real number & a random outcome y in the bollowing - two - stage experiment, finist noll a fain die to get an from the interval corky the probability density Then, 16 Y-K, choose X enibomly The cumulative distribution fonction f(5) and function f(s) of x fd 3 25k4. Jokjib Y= X. we have x as ulk) Ib Y= X. f(x)= The total probability is pa), EP(AB) P(B) w { $yly ak) Yx I(0:2) where fy (y = k) = 16 (probability of getting and any side) w"M) * (64) K-1

SYk it osack lo other wise C: fie su cox), ia pds of v[o,KJ random Variable) fx (N) % [ Iron] W) + yo 90, 9) (a) +... 166.6362] 50 at X = 45 only ten mis (5,6) will nemain fx [45) - %£o + .. +0+ Ślt=1] = % [ - % [%] 20.0611 fx (45) = 0.0611