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A random variable X takes the values 1, 2 and 3 with probabilities 0.3, 0.4 and 0.3…

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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 $1$ , $2$ and $3$ with probabilities $0.3$ , $0.4$ and $0.3$ . Find its mean, its variance and its standard deviation. Give the standard deviation to three decimal places.

Need a reminder? The key ideaShow

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

Have you tried it?

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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