Statistical Techniques for Transportation Engineering

The theoretical (expected) frequencies are

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

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