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A random variable X takes the values 0, 1, 2 and 3…

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Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

A random variable $X$ takes the values $0$ , $1$ , $2$ and $3$ . We know that $P(X = 2) = 0.3$ and $P(X = 3) = 0.1$ , and that $E(X) = 1.3$ . The other two probabilities are unknown. Find $P(X = 1)$ and $P(X = 0)$ . Then find the standard deviation of $X$ .

Need a reminder? The key ideaShow

The expected value is the long-run mean, each value weighted by its probability:

\displaystyle E(X) = \sum x\,P(X = x).

The expected value of a total is the total of the expected values.

The variance is the weighted mean of the squared distances from $\mu$ , and the standard deviation is its square root:

\displaystyle \sigma^2 = \sum (x - \mu)^2 P(X = x) = E(X^2) - \mu^2.

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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