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?
Given : Probability distribution,
Required: The mean and standard deviation
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,