Question

Let X denote the amount of time a book on two-hour reserve is actually checked out, and suppose the cdf is the following.

F(x) = 0 ; x < 0
x²/25 ; 0 < x < 5
1 ; 5 < x

Use the cdf to obtain the following. (If necessary, round your answer to four decimal places)
P(x < 3) (lessthan/equal)

Answer 1

The cumulative distribution function (CDF) is used to find the probability of a book on two-hour reserve being checked out for less than 3 hours.

Step-by-step explanation:

The cumulative distribution function (CDF) of X is defined as P(X ≤ x), which gives the probability that the random variable X is less than or equal to x. In this case, X represents the amount of time a book on two-hour reserve is checked out.

Using the given CDF, we can find P(x < 3) as follows:

1. For x < 0, the probability is 0.
2. For 0 < x < 5, the probability is x2/25.
3. For 5 ≤ x, the probability is 1.

Since 3 falls within the range of 0 < x < 5, we can calculate P(x < 3) by substituting x=3 into the CDF equation:

F(3) = 32/25 = 9/25 ≈ 0.3600