A discrete random variable Y follows a geometric distribution with variance 12. Find the probability of success on a single trial.

Model answer

1/4

Also accepted: 0,25, 0.25, p=1/4, p = 0,25, 0,250, 0.250

Explanation

A geometric distribution with success probability

p

has variance

\dfrac{1-p}{p^{2}}

. Setting

\dfrac{1-p}{p^{2}}=12

gives

12p^{2}+p-1=0

, that is

(4p-1)(3p+1)=0

. A probability cannot be negative, so

p=\dfrac{1}{4}

Derived from ZIMSEC Statistics Paper 4, June 2011, Q1

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