# What are the mean and standard deviation of the probability density function given by #(p(x))/k=x^8-x^16# for # x in [0,1]#, in terms of k, with k being a constant such that the cumulative density across the range of x is equal to 1?

##### 1 Answer

Dec 15, 2016

The mean is

The standard deviation is

#### Explanation:

The probability density function is

We use

Therefore,

The mean is

The standard deviation is

Therefore,