Question

Let 𝑋 and π‘Œ be independent random variables, uniformly distributed on [0,1]. Let π‘ˆ=min{𝑋,π‘Œ} and 𝑉=max{𝑋,π‘Œ}. Let π‘Ž=𝐄[π‘ˆπ‘‰] and 𝑏=𝐄[𝑉].

1. Find π‘Ž. 2. Find 𝑏. 3. Find Cov(π‘ˆ,𝑉).

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

Answers

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

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