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GATE Electrical 2017 Set 2 | Question: 40

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A person decides to toss a fair coin repeatedly until he gets a head. He will make at most $3$ tosses. Let the random variable $Y$ denote the number of heads. The value of $\text{var} \{Y\}$, where $\text{var} \{ \cdot \}$ denotes the variance, equals

  1. $\frac{7}{8} \\$
  2. $\frac{49}{64} \\$
  3. $\frac{7}{64} \\$
  4. $\frac{105}{64}$

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