Question

Let f(x) =3x2 for 0 < x < 1. P(X < 1/2) = P(X <= 1/2)
(A) True
(B) False

Answer 1

The statement 'P(X < 1/2) = P(X <= 1/2)' is false.

Step-by-step explanation:

P(X < 1/2) can be rewritten as P(X ≤ 1/2) for continuous distributions. The cumulative distribution function or CDF, denoted as P(X ≤ x), gives the area to the left of the vertical line through x. In this case, since f(x) = 3x^2 for 0 < x < 1, the area to the left of x = 1/2 is calculated as: P(X ≤ 1/2) = ∫(0 to 1/2) 3x^2 dx = [x^3] from 0 to 1/2 = (1/2)^3 - (0)^3 = 1/8.

Therefore, P(X < 1/2) = P(X ≤ 1/2) ≈ 1/8. Since P(X < 1/2) is not equal to 0.1, the statement is (B) False.