Question

12. (15 points) Let X be a continuous random variable with cumulative distribution function 0, <a Inz, a<<b 1, bsa (a) Find the values of a and b so that F(x) is the distribution function of a continuous random variable. (b) Find P(X > 2). (c) Find the probability density function S(x) for X. (d) Find E(X)

Answer 1

0 Question cod-f ofx, F(x)= @ ; aca logy ; acacb ; asb rie a=1 - Answer Auswer By the proporty of cod-f. ; Fla) = 0 and Flb) =/ F(a)=0 gives log a i.e. aze F(b) =) gives b=e bog loge b = 1 ie bze' ie ;*</ Thus, Ciday, ofx, F(x) = loge; kace ; as, e P& (x>2) = 1-Ps (x <2) - 1-F(2) = 1 - loge? = 1–14(2) 0 I - Answer Auswer -1-0.693147101 = 0.306852819 Flac) = i 1<x<e otherwise ) Fanswer

@ E(X)= S zgrade = 3 Spoden fer ser funde-cefont (7 = 2.71828183-1 1,71828103 Auswer