2. Let T = ∞ 1/i2 i=1 . Recall 0 < T ≤ 2.

Let Y be defined as follows:

⎧

⎪⎨

Y = i, if i is even, with probability 1/Ti 2

y = = −i, if i is odd, with probability 1/Ti 2

= 0 otherwise

(a) Show that Y is a random

⎪⎩

variable, that is, show

∞

P Y = i = 1.

i=

n { }

−∞

(b) Does E(Y ) exist? Explain why or why not.