Question

The cdf of checkout duration X for a book on a 2-hour reserve at a college

library is given by The CDF:
0 X< 0, F(x)= x²/4 0≤x< 2and 1 for 2≤x
Use this cdf to compute the following:
a. P(X≤1)

Answer 1

The probability that the checkout duration of a book on a 2-hour reserve at a college library is less than or equal to 1 is 1/4.

Step-by-step explanation:

The cumulative distribution function (CDF) for the checkout duration of a book on a 2-hour reserve at a college library is given by:

F(x) = 0, for X < 0

F(x) = x²/4, for 0 ≤ x < 2

F(x) = 1, for 2 ≤ x

To find P(X ≤ 1), we need to evaluate the cumulative distribution function at x = 1.

Using the CDF:

P(X ≤ 1) = F(1) = (1²/4) = 1/4