Suppose an investor faces a risk x that is uniformly distributed over [-1,1]. She is exposed to another risk y (on her labor income) that is independent from x . The payoffs of y are distributed as:

-1 with probability 1/2

4 with probability 1/4 -2.5 with probability 1/4

Is y a MPS (Mean Preserving Spread) of x ? Justify your answer with calculations. (Hint: No need to compute the integral condition. The mean of a uniform random variable over [a,b] is equal to (a + b)/2 and the variance equal to (b a)2/12).