6. For the random variable X with density function
f(x) =
4x, 0 < x < 1
0, otherwise
Determine the distribution function F(x), and draw the graphs f(x) and F(x). Determine P(a < X < b). Determine E[X]. Determine Var(X), and σ(X).
SOLUTION:
For x ∈ [0, 1]: F(x) = ∫4x dx = 2x^2 = 2x^2
For x > 1: F(x) = ∫4-4x dx = 4x - 2 = 4x - 2
P(a < X < b) = ?
E[X] = ?
Var(X) = ?
σ(X) = ?