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Assume that the aggressive invasive tree known as European Buckthorn is randomly distributed in a degraded forest preserve with λ =40 trees/seedlings per 100m^2. If two 100 m^2 plots are randomly chosen then what is the probability that one of the plots has at least 30 buckthorn trees/seedlings while the other plot has 30 or less such trees?

I have no idea where to start from, any idea ??

kingjames
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1 Answers1

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Well, start by assuming r.v. X be the number of European Buckthorn per 100m^2. So, X follows Poisson(40). Now since the two plots are randomly chosen, their selections are independent of each other. So, the required probability is

P(X>=30)*P(X<=30)

={1-P(X<30)}*P(X<=30)

Now, the calculation is tedious. I used excel to calculate (using pmf of exponential distribution), the result is approximately 0.059027.

Also, using normal approximation, we get an approximate probability as 0.05368.

StatnNumber
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