# What are the mean and standard deviation of the probability density function given by #p(x)=x^4-x^3+1# 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

1)

Thus

2)

3)

#### Explanation:

**Given** : Probability distribution,

**Required**: The mean and standard deviation

**Solution Strategy**:

1) First ensure you have a probability distribution function in the interval [0,1] by normalizing p(x),

2) Use the mean integral equation,

3) Use the variance integral,

**Solution**:

1)

Thus

2)

3)