1. 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?

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

  2. The probability that a man in a certain age group dies in the next four years is $\displaystyle {{1}\over{50}}$. Suppose that we study 100 men. Then approximately find the probability that 2 of them or fewer die in the next four years.

    $\displaystyle e^ {- 2 }$ $\displaystyle 3\,e^ {- 2 }$ $\displaystyle {{1}\over{50}}$ $\displaystyle 5\,e^ {- 2 }$

  3. 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 one suiside in one year?

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

  4. 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 average number of suicides in one year?

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

  5. Professor Rice was told that he has only 1 chance in 10,000 of being trapped in a much-maligned elevator in the mathematics building. Assume that the outcomes on all the days are mutually independent. If he goes to work 5 days a week, 50 weeks a year, for 30 years and always rides the elevator up to his office when he first arrives. What is the probability that he will be trapped twice ?

    $\displaystyle e^ {- {{3}\over{4}} }$ $\displaystyle {{3\,e^ {- {{3}\over{4}} }}\over{4}}$ $\displaystyle {{3}\over{4}}$ $\displaystyle {{9\,e^ {- {{3}\over{4}} }}\over{32}}$


Department of Mathematics
Last modified: 2024-01-21