Variance of a compound daily total

MediumRandom Variables~5m

The number of trades you fill in a day is Poisson with mean $5$ . Each trade's size is independently equally likely to be $1$ , $2$ , or $3$ lots, independent of how many trades there are. What is the variance of your total daily volume (in lots $^2$ )? Give a decimal to four places.

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A random number of random sizes - use the law of total variance.
For a Poisson count, $\operatorname{Var}(S)=\lambda E[X^2]$ .

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23.3333 (± 0.01)

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Variance of a compound daily total

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