[singh2010]

I have two formulas for the mean and variance of binomial distribution, the success with probability p and failure with probability 1-p
It says on what I have been given that the mean and variance for the number of successes in n trials are given by:

mean = n x p:
variance = n x p x (1-p)

Is this for both successes and failures as above it just says successes in n trials so I am just a bit confused.

Thanks

[Unknown008]

Ok, I'll give you an example.

Say the probability for success is 0.25, that for failure will be 1 - 0.25 = 0.75. Let n = 10.

Mean success = 10 x 0.25 = 2.5
Variance of success = 10 x 0.25 x 0.75 = 1.875

Now, let's find the ones for failure.

Mean failure = 10 x 0.75 = 7.5
Variance of failure = 10 x 0.75 x 0.25 = 1.875

As you can see, the mean is different, but the variance is the same! :)

[singh2010]

Thanks for the help. Much appreciated.

[Unknown008]

You're welcome :)