Answer

For the mosquito, \(P(bite) = P(land)P(bite \vert land) = 0.1\). \(X\) is a geometric random variable. \(E[X] = 1/p = 10\) and \(Var(X) = \frac{1-p}{p^{2}} = 90\).

For the mosquito and tick combined, \(P(\)mosquito or tick\() = 0.1 + 0.1 \times 0.7 - 0.1 \times 0.1 \times 0.7 = 0.163\). This is again a geometric random variable with \(E[Y] = 1/0.163\) and \(Var(Y) = (1-0.163)/(0.163^{2})\).