1. Suppose that in a city the number of suicides can be approximated by a Poisson random variable with $\lambda = {{2}\over{3}}$ per month. What is the probability of two suicides in one year?

    $\displaystyle 32\,e^ {- 8 }$ $\displaystyle e^ {- 8 }$ $\displaystyle 8\,e^ {- 8 }$ $\displaystyle {{2}\over{3}}$

  2. Suppose that a rare disease has an incidence of $1$ in $1000$. and that members of the population are affected independently. Let $X$ be the number of cases in a population of 10000 What is the average number of cases?

    $\displaystyle 10\,e^ {- 10 }$ 10000 10 $\displaystyle e^ {- 10 }$

  3. Suppose that in a city the number of suicides can be approximated by a Poisson random variable with $\lambda = {{1}\over{3}}$ per month. What is the average number of suicides in one year?

    4 $\displaystyle {{1}\over{3}}$ $\displaystyle 4\,e^ {- 4 }$ $\displaystyle e^ {- 4 }$

  4. The probability that a man in a certain age group dies in the next four years is $\displaystyle {{1}\over{100}}$. Suppose that we study 20 men. Then approximately find the probability that 1 of them or fewer die in the next four years.

    $\displaystyle e^ {- {{1}\over{5}} }$ $\displaystyle {{61\,e^ {- {{1}\over{5}} }}\over{50}}$ $\displaystyle {{6\,e^ {- {{1}\over{5}} }}\over{5}}$ $\displaystyle {{1}\over{100}}$

  5. The probability of being dealt a royal straight flush (ace, king, queen, jack, and ten of the same suit) in poker is about $1.5\times 10^{-6}$. Suppose that an avid poker player sees $200$ hands a week, $50$ weeks a year, for 10 years. What is the probability that she sees at least one royal straight flush dealt?

    $\displaystyle e^ {- {{3}\over{20}} }$ $\displaystyle 1-e^ {- {{3}\over{20}} }$ $\displaystyle {{3}\over{20}}$ $\displaystyle 1-{{23\,e^ {- {{3}\over{20}} }}\over{20}}$


Department of Mathematics
Last modified: 2025-03-28