Consider the following frequency table of observation on the

Consider the following frequency table of observation on the random variable X.

Values

0

1

2

3

4

5

Observed Frequency

8

25

23

21

16

7

Based on these 100 observations, is a Poisson distribution with a mean of 2.4 an appropriate model? Perform a goodness-of-fit procedure with
Calculate the P-value for this test. show youre work for this

Solution

Note that for Poisson distribution,

P(x) = (lambda)^x exp (-lambda) / x!

where lambda = mean = 2.4.

Thus, the expected frequencies of each must be

f(x) = n P(x) = 100 P(x)

Thus, the expected values are

Expected Freqquencies

9.071809974
21.77234394
26.12681273
20.90145018
12.54087011
6.019617652

Thus, using

chi^2 = Sum[(O - E)^2 / E)

Thus,

chi^2 = 2.093590152

Thus, using technology to get the p value,

p = 0.836049405 [ANSWER]