In the last example, we saw that the conditional distribution of 𝑋, which was a uniform over a smaller range (and in some sense, less uncertain), had a smaller variance, i.e., 𝖵𝖺𝗋(𝑋∣𝐴)≤𝖵𝖺𝗋(𝑋). Here is an example where this is not true. Let 𝑌 be uniform on {0,1,2} and let 𝐵 be the event that 𝑌 belongs to {0,2}.

Question

a) What is the variance of 𝑌?

𝖵𝖺𝗋(𝑌)=

Answer 1

(a) 2/3
(b) 1