The variance of a random variable has to be greater than or equal to zero. It equals zero if and only if the random variable is a constant with probability 1. The kurtosis of a random variable X is...

The variance of a random variable has to be greater than or equal to zero. It equals zero if and only if the random variable is a constant with probability 1. The kurtosis of a random variable X is often defined as

It is a measure of the likelihood of outliers for the random variable X. In general, the bigger the kurtosis is, the more likely outliers will occur. Show that the uniform distribution defined in problem 4 has minimum kurtosis. (Hint: What is the variance of U2 ?)