Statistical Methods

Unit 2 - Probability distributions

2.5.Fitting of Binomial distribution
To fit any theoretical distribution one should know its parameters and probability distribution. Parameters of Binomial distribution are n and p. Once p and n are known, binomial probabilities for different random events and the corresponding expected frequencies can be computed. From the given data we can get n by inspection. For binomial distribution, we know that mean is equal to np hence we can estimate p as = mean/n .Thus with these n and p one can fit the binomial distribution.
Example 4
The number of sets of catla which responded in induced breeding out 10 fishes tried per experiment was noted. A total of 100 such experiments were conducted in a centre. The results are summarised in the following frequency distribution table:

Fit the binomial distribution .
Answer
Here n = 10, ∑f = 100 = N


Computations are summarized below:

* Expected frequency = N P (x)