image

The theoretical (expected) frequencies are

NP(0)=(120)(0.22313)=27,NP(1)=(120)(0.334695)=40,NP(2)=(120)(0.25)=30,NP(3)=(120)(0.13)=16,NP(4)=(120)(0.05)=6,NP(5)=(120)(0.01)=1

image

i.e., 27, 40, 30, 16, 6, and 1.

Example 4.73: If X and Y are two independent random Poisson random variables such that Var[X]+Var[Y]=3. Find P(X+Y<2)?

Solution: Let X and Y follow Poisson distribution.

Let λ1 be the mean of X and λ2 be the mean of Y.

Then by additive property X+Y follows Poisson distribution with mean λ1+λ2.

We have Var[X]+Var[Y]=λ1+λ2=3(given)

λ=λ1+λ2

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