Let 𝑋 and 𝑌 be independent random variables, uniformly distributed on [0,1]. Let 𝑈=min{𝑋,𝑌} and 𝑉=max{𝑋,𝑌}. Let 𝑎=𝐄[𝑈𝑉] and 𝑏=𝐄[𝑉].

Question

1. Find 𝑎. 2. Find 𝑏. 3. Find Cov(𝑈,𝑉).

You can give either a numerical answer or a symbolic expression involving 𝑎 and 𝑏. (There are many possible equivalent answers.)

Answer 1

1. 1/4
2. 1/2
3. 0