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Math Help - poisson process probability distribution

  1. #1
    Newbie emterics90's Avatar
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    poisson process probability distribution

    A shop receives sales according to a Poisson process \{N_t : t \ge 0\} with rate \lambda=1 per minute and suppose each sale, independently of the others, has probability 0.05 of being from a male and probability 0.95 of being from a female.

    I'm trying to get the distribution of the number of females sales in the shop in the time interval [0,t].

    I'm guessing you'd use a Poisson distribution. Someone told me you use an exponential distribution but the exponential is for the times between sales. So I am thinking that the fact that the sales have 0.95 probability of being female affects the rate \lambda. So then x the number of female sales in the shop from 0 to t is distributed

    f(x)=\frac{e^{-0.95 \lambda t}(0.95 \lambda t)^x}{x!}

    Would this be right?
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by emterics90
    A shop receives sales according to a Poisson process \{N_t : t \ge 0\} with rate \lambda=1 per minute and suppose each sale, independently of the others, has probability 0.05 of being from a male and probability 0.95 of being from a female.

    I'm trying to get the distribution of the number of females sales in the shop in the time interval [0,t].

    I'm guessing you'd use a Poisson distribution. Someone told me you use an exponential distribution but the exponential is for the times between sales. So I am thinking that the fact that the sales have 0.95 probability of being female affects the rate \lambda. So then x the number of female sales in the shop from 0 to t is distributed

    f(x)=\frac{e^{-0.95 \lambda t}(0.95 \lambda t)^x}{x!}

    Would this be right?
    Looks OK to me.

    RonL
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