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    In a country the mean number of deaths per year from lightning strike is 2.2.

    First part of question ask to find probability of 0,1,2 >2 deaths. That was easy. X ~ Poisson(2.2) and calculate probabilities. I had no problem with that.

    But next part of question is as follows.

    In a neighbouring country, it is found that one year in 20 nobody dies from lightning strike. What is the mean number of deaths per year in that country from lightning strike?

    Thinking through this one, do they mean that because it is neighbouring that mean per year is still 2.2 but every 20th year there is no death. so 19 x 2.2 + 0 = 41.8. 41.8/20 = 2.09 which is mean for this neighbouring country. But that in fact is incorrect answer. answer should be 3.

    I know from question that in neighbouring country 1 year in 20 there are no deaths. But I don't know how many deaths there are in the other 19 years in 20. So how is it possible to work this out? What am I missing here?
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    (Original post by acomber)

    In a neighbouring country, it is found that one year in 20 nobody dies from lightning strike. What is the mean number of deaths per year in that country from lightning strike?

    Thinking through this one, do they mean that because it is neighbouring that mean per year is still 2.2 but every 20th year there is no death. so 19 x 2.2 + 0 = 41.8. 41.8/20 = 2.09 which is mean for this neighbouring country. But that in fact is incorrect answer. answer should be 3.

    I know from question that in neighbouring country 1 year in 20 there are no deaths. But I don't know how many deaths there are in the other 19 years in 20. So how is it possible to work this out? What am I missing here?
    Assuming it's Poisson again, then you have P(X=0)=0.05.

    So, what value of lambda gives that. I.e. what's the formula for P(x=0) in terms of lambda. And solve.
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    (Original post by ghostwalker)
    Assuming it's Poisson again, then you have P(X=0)=0.05.

    So, what value of lambda gives that. I.e. what's the formula for P(x=0) in terms of lambda. And solve.
    Thank you.

    ie

    P(X = 0) = e^{-\lambda} = 0.05

    let l = lambda

    log(e^-l) = log(0.05)

    -l log(e) = log(0.05)

    lambda = -log(0.05)/loge = 3
 
 
 
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