A random variable X is continuous and bounded between zero and five, X:(0 ≤ X ≤ 5). The cumulative distribution function (cdf) for X is F(x) = x / 5. Calculate P(2 ≤ X ≤ 4). A. 1.00. B. 0.40. C. 0.50.
For a continuous distribution, P(a ≤ X ≤b) = F(b) − F(a). Here, F(4) = 0.8 and F(2) = 0.4. Note also that this is a uniform distribution over 0 ≤ x ≤ 5 so Prob(2 < x < 4) = (4 − 2) / 5 = 40%.
