Results 1 to 2 of 2
Like Tree1Thanks
  • 1 Post By romsek

Thread: Poisson Distribution

  1. #1
    Newbie
    Joined
    Mar 2017
    From
    USA
    Posts
    11

    Poisson Distribution

    Given 400 people, estimate the probability that 3 or more will have a birthday on July 4. Assume there are 365 days in a year and each is equally likely to be the birthday of a randomly chosen person.

    I have already tried to solve this problem and got e^-3 but that is not correct. I am unsure of where I messed up in my calculations so if you could show step by step then that would be helpful.

    And also, how does that calculation differ from this question:
    Calculate the probability that at most 1 person in 500 will have a birthday on Christmas. Assume there are 365 days in a year.

    Thank you in advance!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Nov 2013
    From
    California
    Posts
    5,525
    Thanks
    2332

    Re: Poisson Distribution

    I guess the rate will be $\lambda = \dfrac{400}{365}$

    $\begin{align*}

    &\phantom{=}P[\text{at least 3 have birthday on July 4}] \\
    &= 1 - P[\text{less than 3 have birthday on July 4}] \\
    &= 1 - e^{-\lambda}\left(1+\lambda+\dfrac{\lambda^2}{2}\right ) \approx 0.09876

    \end{align*}$

    for (2) the rate becomes $\lambda = \dfrac{500}{365}$

    $P[\text{at most 1 person has birthday on Christmas}] = e^{-\lambda}\left(1+\lambda\right) \approx 0.6023$
    Thanks from ballerninja29
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Binomial Distribution vs Poisson Distribution
    Posted in the Statistics Forum
    Replies: 1
    Last Post: Apr 4th 2015, 08:04 PM
  2. Replies: 1
    Last Post: Feb 23rd 2015, 07:58 AM
  3. Binomial distribution va. Poisson distribution
    Posted in the Statistics Forum
    Replies: 2
    Last Post: Nov 9th 2012, 05:41 AM
  4. Replies: 1
    Last Post: Dec 27th 2011, 01:08 PM
  5. Poisson distribution and asymptotic normal distribution.
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: Aug 18th 2010, 05:52 AM

/mathhelpforum @mathhelpforum