The Binomial Distribution
The binomial distribution is a distribution which works for any set of events which has:
A fixed number of trials
Only two possible outcomes from each trial
The same probability for each outcome from each trial
Trials independent of each other
E.g. I flip a coin. It is either heads or tails. It cannot be both and it cannot be anything other than heads or tails. We can also say that I will achieve a result of heads or not heads.
To make this into a binomial distribution, we need to know a few things.
Number of trials = n
Number of successes = r
Probability of success = p
Probability of failure = q
This leads us to the equation:
P(X=r) = (nCr)(p^r)(q^(n-r)) where X ~ B(n, p)
x ~ B(n, p) simply means X is distributed binomially with number of trials, n, and probability of success, p.
If you have a graphical calculator which has a statistics setting, go to that and then find:
BcD (which gives you X=r)
BpD (which gives X ≤ r)
Mean and Variance
The mean and variance of the binomial distribution can be found easily using nothing more than n and p.
Mean = np
Variance = np(1-p)
The standard deviation of the binomial distribution can be found by taking the square root of the variance.
These two can be found in the formula book on…