|A5 The random variable X has the geometric distribution with probability mass function (pmf) Px(x) = q*p, x = 0, 1,2, ... 0

|A5<br>The random variable X has the geometric distribution with probability mass function (pmf)<br>Px(x) = q*p, x = 0, 1,2, ... 0 < p < 1,<br>where q = 1-p<br>i)<br>Find P(X 2 x) and show that P(X < 3) =1 – q*.<br>ii)<br>Explain why<br>P[X is odd(= 1,3,5,7, ...] = q × P[X is even(= 0,2,4,6, ..)]<br>And hence otherwise show that<br>P(X is odd ) =<br>1+9<br>iii)<br>Find P(X is odd|x < 3) as a function of q, and, given that<br>

Extracted text: |A5 The random variable X has the geometric distribution with probability mass function (pmf) Px(x) = q*p, x = 0, 1,2, ... 0 < p="">< 1,="" where="" q="1-p" i)="" find="" p(x="" 2="" x)="" and="" show="" that="" p(x="">< 3)="1" –="" q*.="" ii)="" explain="" why="" p[x="" is="" odd(="1,3,5,7," ...]="q" ×="" p[x="" is="" even(="0,2,4,6," ..)]="" and="" hence="" otherwise="" show="" that="" p(x="" is="" odd="" )="1+9" iii)="" find="" p(x="" is="" odd|x="">< 3)="" as="" a="" function="" of="" q,="" and,="" given="">

Jun 08, 2022

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|A5 The random variable X has the geometric distribution with probability mass function (pmf) Px(x) = q*p, x = 0, 1,2, ... 0

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