Poisson distribution has following PDF:
P(X=k)=k!λke−λ
We can use given value P(X=0)=0.2 to find the value of λ.
P(X=k)=11e−λ=0.2
λ=−ln0.2=1.609, and, since the coefficient e−λ is the same for every X=k, we can use directly e−λ=0.2.
P(X>2)=1−P(X≤2)=1−P(X=0)−P(X=1)−P(X=2)
P(X=0)=0.2
P(X=1)=11.6090.2=0.322
P(X=2)=2⋅11.60920.2=0.259
So, P(X>2)=1−0.2−0.322−0.259=0.219
Answer: P(X>2)=0.219
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