Practical Exercise -1
Fitting of Binomial
Distribution (Direct Method)
1.
Eight coins are tossed
at a time 256 times. Number of heads observed at each throw is recorded and the
results are given below. Fit the binomial distribution to this data by assuming
(i) when the coin is unbiased and (ii) when the nature of the coin is not known
using direct method
|
No. of Heads |
0 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
|
Frequency |
2 |
6 |
30 |
52 |
67 |
56 |
32 |
10 |
1 |
2.
The following data shows that the number of seeds
germinating out of 10 dump filter for 80 sets of seeds. Fit the binomial
distribution to this data by direct method
|
X |
0 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
|
Y |
6 |
20 |
28 |
12 |
8 |
5 |
0 |
0 |
0 |
0 |
0 |
3. The screws produced by
certain machines were checked by examining samples of 12. The following table
shows the distribution of 128 samples according to the number of defective
items they contained if the chance of machine being defective is ½.
|
No. of defectives in a sample of 12 |
0 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
|
No. of samples |
7 |
6 |
19 |
35 |
30 |
23 |
7 |
1 |
Fit
a binomial distribution by direct method
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