The theoretical (expected) frequencies are

$\begin{array}{ll}NP\left(0\right)\hfill & =\left(120\right)\left(0.22313\right)=27,\hfill \\ NP\left(1\right)\hfill & =\left(120\right)\left(0.334695\right)=40,\hfill \\ NP\left(2\right)\hfill & =\left(120\right)\left(0.25\right)=30,\hfill \\ NP\left(3\right)\hfill & =\left(120\right)\left(0.13\right)=16,\hfill \\ NP\left(4\right)\hfill & =\left(120\right)\left(0.05\right)=6,\hfill \\ NP\left(5\right)\hfill & =\left(120\right)\left(0.01\right)=1\hfill \end{array}$

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

Get Statistical Techniques for Transportation Engineering now with the O’Reilly learning platform.

O’Reilly members experience books, live events, courses curated by job role, and more from O’Reilly and nearly 200 top publishers.