the mean and variance of a random variable X, that has a continuous uniform distribution within the interval a

the mean and variance of a random variable X, that has a continuous unifonn distribution witmn the Interval a X S b, are given by: 02 = = 2 12 (a) Apply the definition for the mean and the variance Of a random variable to proof that the two formulas above are correct; (b) Compute the third and fourth raw and central moment of X ; and (c) What is the skewness and kurtosis of X? (d) How do you interpret skewness and kurtosis, i.e. what information about the distribution Of a random variable do these two metrics express?