Question

A student has six friends in a Probability course, only three of which have the expertise to answer the last question on an assignment. Suppose that the student calls their 6 friends in the course, in a random order,until they reach a friend that can help them solve the assignment question. Let the random variable X represent the number of calls made by the student.a.Determine the probability function of X. Determine the cumulative distribution function of X. c.What is the expected number of friends called by the student? d.What is the variance of the number of friends called by the student?

Answer 1

{ expert & → Not an expert No of calls 044 Ex expert & Nor an expert a(z) (ab | elek E() - Noref cada = 2 &(?) Noof cales o 8 (1) - No of all No of calli 3 Calls a friend 1 x = 1 20 - X = no of calls untill solved Probability function a) P(x= 1) = 3= P(X=2) = {x}= P(X=3) - Zxzxz - 3 P(X=4) = 2*XXI = 20 b) Cumulative func" • F(n=n) = P(x x ) F(x=1) = ? Flan=2) = +?= $_=4 c) E(X)= Expex) = 1xĻ+ 2x + 3x2 + 4 zo {+ 7 + 3 + 1 - 10+ 12+ + 4 35 20 E 175 no.of calls Flu=3) = { + } + že se FCM=4)= Scanned with CamScanner

d) Varcx) = ECX ixt +4x3 + 9x31 16X1 To 20 = 10 +24 + 27+- CS Scanned with 0-7875 CamScanner 07875 sh ch 20