Question

This is a written question, worth 15 points. DO NOT place the problem code on the answer sheet. A proctor will fill this out after exam submission. Show all steps (work) on your answer sheet for full credit. Problem Code: 1123 Assume the length X in minutes for a phone conversation is a random variable with probability density function: f(x) = { ce-116 x > 0 elsewhere

Answer 1

Given, © We know, .) dn = 1 Armed ced, men *** ()= } so when He knows sind din = 1 » Doe-% dar a => c. 6.[-e-47*24 = 6c ( 0 + 1) = 1 -> c= Ś 70 - -919 C. © Pl* > B) 10 a = 0.0498. 1- P(x+18) i ce- * da -i-et-6.-98765 EL-C[-669+6] -1-(-ei+1) © £[*] = sooncent dans osoa em de = (3.1 91e mall - $7.(-5) e-Yo du. = (- ze=93)*+ 5.16% de = (-6e-Welle = 0 +6.

D E (*2). 5. ** cent du = tra xe % da 75 22. (6) = 12c se ne da = 12x6 = 72 van *) = E(X) - ( EX)) - 72- 62 36. SD (X) = van (*) = 36 = 6 P ( en E(A) - 2.5D1%) < x < €1x) +2.50(x)) = P l 6 - 2x6 < x < 6+ 286) =pl-6 <x< 18). a plouxcis) be cause xx0. = Sce-175 do z des = 0.9502 E [ (*+5)] - E [ ** + 10x+25] = E [*2] + 10 E[x] + 25 = 72 + 10x6 +25 = 157 Ans.
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