Question

A random number generator will spread its output uniformly across the entire interval from 0 to 1 as we allow it to generate a long sequence of numbers. The results of many trials are represented by the density curve of a uniform distribution. This density curve appears in red in the given figure. It has height 1 over the interval from 0 to 1, and height 0 everywhere else. The area under the density curve is 1: the area of a square with base 1 and height 1. Let the random variable  be a random number with the uniform density curve in the given figure. The probability of any event is the area under the density curve and above the event in question. As Figure (a) illustrates, the probability that the random number generator produces a number X between 0.3 and 0.7 is P(0.3 ≤ X ≤ 0.7) = 0.4 because the area under the density curve and above the interval from 0.3 to 0.7 is 0.4. The height of the density curve is 1, and the area of a rectangle is the product of height and length, so the probability of any interval of outcomes is just the length of the interval. Similarly, P(X ≤ 0.4) = 0.4 P(X > 0.8) = 0.2 P(X ≤ 0.4 or X > 0.8) = 0.6 Step 1: Find the following: P(X ≥ 0.3) = _______ . P(X ≤ 0.3) = _______ . P(X > 0.3) = _______ . P(X < 0.3) = _______ . P(X = 0.3) = _______ . Step 2: Find the following: P(0.25 < X ≤ 0.6) = _______ . P(0.6 ≤ X < 1.3) = _______ . P(X < 0.15 or X > 0.8) = _______ . P(X < 0.3 and X > 0.7) = _______ .

Answer 1