Springer Texts in Business and Economics

The Uniform Density

a. e(x) = У xdx = |[x2]0 = 2 E(x2) = /с - x2dx = 3 ИІ = 3

so that var(X) = E(X2) - (E(X))2 = - - - = 4=3 = .

b. Pr[0.1 < X < 0.3] = /У dx = 0.3 — 0.1 = 0.2. It does not matter if we include the equality signs Pr[0.1 < X < 0.3] since this is a continuous random variable. Note that this integral is the area of the rectangle, for X between 0.1 and 0.3 and height equal to 1. This is just the length of this rectangle, i. e., 0.3 — 0.1 = 0.2.