The theoretical (expected) frequencies are
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)