A city has an average 2.3 children per family. Randomly chosen child has avg of 1.6 siblings. Determine variance of number of children

Question

A city has an average 2.3 children per family. Randomly chosen child has avg of 1.6 siblings. Determine variance of number of children in a random family

I'm assuming it's the 2 Poisson's multiplied together then get their expectation, which is

$$2.3^ke^{-2.3}/k!$$ $$1.6^ke^{-1.6}/k!$$

E[X*Y]=E[X]*E[Y]=2.5*1.6
But this seems off.

Answer 1

There's no Poisson distribution here.

Hint: If $X$ is the number of children in a family in this population, you're told $\mathbb E[X] = 2.3$, and $\mathbb E[X (X-1)]/\mathbb E[X] = 1.6$. Find $\mathbb E[X^2]$ and then the variance.