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At a school fair, a spinner game pays 0 rupees with probability 0.5, 10 rupees with probability 0.3…

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At a school fair, a spinner game pays $0$ rupees with probability $0.5$ , $10$ rupees with probability $0.3$ and $20$ rupees with probability $0.2$ . Let $X$ be the payout in rupees. Find the mean payout, the variance of the payout and its standard deviation. A player pays $8$ rupees to play once. Find the expected net gain of the player.

Need a reminder? The key ideaShow

For a distribution, $E(X) = \sum x\,p$ and $\text{Var}(X) = E(X^2) - [E(X)]^2$ with $E(X^2) = \sum x^2\,p$ . For $aX + b$ , the mean is $aE(X) + b$ and the variance is $a^2\,\text{Var}(X)$ .

The worked solution

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Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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