Question

6. For a certain section of a pine forest, the number X of diseased trees per acre has a Poisson distribution with mean λ = 5.

(C) Suppose we have 4 plots of forest, each one acre in size, giving 4 independent Poisson random variables, X1, X2,..., X4 with mean λ = 5. Find the probability that at least two of the plots of forest have 2 or more diseased trees per acre.

Answer 1

J for centain Section of pine fores! to the number of diseased Hopes per acre has poisson distoibution with mean = 5 Suppose there are 4 plots each of deacre then 4 independent poisson ru associted with each plot with 1-5 to find the probability that at least two of the plots of forest have 2 or more Diseased tress pero aceo let yo is I if ith plot have 2 og mode diseased toegs per acoe 0060L es Yiig Binemal PV where pe Bernuli is to find let y = Eyi - has Binomial Digth with B (n=4, f = 2 has to find) Now P = poobability that 2 of more Diseaged tress per aces . P(X), 2) as xr) Poisson - P(x<2) - - [PCXEO) + P(x-1)] Tel 3- O gºre st) = 095953

Now to find at least two of plots of forest have 200 modė diseased toee per acge. PY 22) yrs Binomial (4,P=0.959|7 y 2 B (n=4, P=0-95957) Py32 ezy - PCy<2) P4-4C, D G DE -P(9=0)+ P(4=1) Ly= 20, 1, 2..4} - - 10.oooto-0025) 0.99972 1. given poobability is 0.99974