# What are the mean and standard deviation of the probability density function given by #(p(x))/k=x^3-4x# for # x in [0,2]#, 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

The mean is

#### Explanation:

If

Hence, the density function is

The mean is the expected value of

The expected value of

Hence, the variance is

The standard deviation is