Fitting Poisson Distribution
We get the relative frequencies by dividing each frequency by the total frequency. If the number of choco chips is described by a Poisson distribution, then should be equal to the mean of the sample. We get the following table:
x | frequency(f) | relative freq | xf |
16 | 1 | 0.05 | 16 |
17 | 1 | 0.05 | 17 |
18 | 1 | 0.05 | 18 |
19 | 2 | 0.1 | 38 |
20 | 2 | 0.1 | 40 |
21 | 0 | 0 | 0 |
22 | 0 | 0 | 0 |
23 | 5 | 0.25 | 115 |
24 | 5 | 0.25 | 120 |
25 | 1 | 0.05 | 25 |
26 | 0 | 0 | 0 |
27 | 1 | 0.05 | 27 |
28 | 1 | 0.05 | 28 |
29 | 0 | 0 | 0 |
30 | 0 | 0 | 0 |
Total | 20 | 1 | 444 |
So the mean is given by: = 444/20 = 22.2.
Thus 22.2.
Now we will calculate the mass values.
We know that the pmf of Poisson distribution is given by: f(x) = exp(-)./ !
So putting 22.2 we get:
x | f(x) |
16 | 0.04 |
17 | 0.05 |
18 | 0.06 |
19 | 0.07 |
20 | 0.08 |
21 | 0.08 |
22 | 0.09 |
23 | 0.08 |
24 | 0.08 |
25 | 0.07 |
26 | 0.06 |
27 | 0.05 |
28 | 0.04 |
29 | 0.03 |
30 | 0.02 |
Thus third option is the correct one.
one question 2 pictures 2.4.8, pp 97 101. A student counts the number of chocolate chips...
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