GATE 2017 EE (EE2) – Question 50

Engineering Mathematics · Probability and Statistics: Random variables · 2 marks · Multiple choice

A fair coin is tossed until a head appears, with at most three tosses. Y is the number of heads obtained. Its variance is

$7/8$
$49/64$
$7/64$
$105/64$

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Correct answer: (C) $7/64$

Explanation

Stopping at the first head means Y can only be 0 or 1. Y=0 occurs exactly for three tails, with probability 1/8. Therefore P(Y=1)=7/8.

Y is Bernoulli with parameter 7/8, so $\operatorname{var}(Y)=p(1-p)=(7/8)(1/8)=$ **7/64, C**. It is not a three-trial binomial count because tossing stops early.

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