Question: The Uniform density, defined over the unit interval [0, 1], assigns a unit probability for all values of X in that interval. It is like

The Uniform density, defined over the unit interval [0, 1], assigns a unit probability for all values of X in that interval. It is like a roulette wheel that has an equal chance of stopping anywhere between 0 and 1.

f(X) = 1 0 ≤ X ≤ 1

= 0 elsewhere Computers are equipped with a Uniform (0,1) random number generator so it is important to understand these distributions.

(a) Show that E(X) = 1/2 and var(X) = 1/12.

(b) What is the Pr[0.1< X < 0.3]? Does it matter if we ask for the Pr[0.1 ≤ X ≤ 0.3]?

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