A ticket pays 10 dollars with probability 1/5 and nothing otherwise. What is the variance of its payout?

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Scratch ticket variance

Expected valueEasy

A ticket pays $10$ dollars with probability $\frac{1}{5}$ and nothing otherwise. What is the variance of its payout?

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Hint

The payout is a scaled win-or-lose indicator.

Solution

The payout is $10$ times an indicator that equals $1$ with probability $\frac{1}{5}$ .
The indicator has variance $\frac{1}{5} \times \frac{4}{5} = \frac{4}{25}$ .
Scaling by $10$ multiplies the variance by $100$ , giving $100 \times \frac{4}{25} = 16$ .

Answer: $16$