See the previous exercise. Suppose ? = 10 and ? = ? = 1. It might be tempting to believe that the distribution of Z is normal with mean 10 and variance 20. (Why might someone make this mistake?) Give visual evidence that this is not the case by simulating the distribution of Z and superimposing a normal density curve with mean 10 and variance 20.

Data from previous exercise.

Let N be a Poisson random variable with parameter ?. Write a one-line R command for simulating

where X₁,X₂, . . . are i.id. normal random variables with parameters ? and ?².

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X;. Z- Σ Χ., , i=1