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Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
Suppose random variable $X$ has possible values $1,2,3,\dots$ and $P(X=j)=\frac{1}{2^j}$, $j=1,2,3,\dots$ then $P(X \text{ is even})$ equals
Solution
Even values: $2,4,6,\dots$
$P(\text{even})=\frac{1}{2^2}+\frac{1}{2^4}+\frac{1}{2^6}+\dots$
$=\frac{1}{4}+\frac{1}{16}+\frac{1}{64}+\dots$
This is geometric series:
$=\frac{1/4}{1-1/4}=\frac{1/4}{3/4}=\frac{1}{3}$
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