Let X denote the amount of time a book on two-hour reserve is actually checked out, and suppose the cdf is the following. x < 0 x2 F(x) = 0 sx < 5 25 1 Use the cdf to obtain the following. (If necessary, round your answer to four decimal places.) (a) Calculate P(X < 3). 0.04 (b) Calculate P(2.5 s X s 3). -0.21 (c) Calculate P(X > 3.5). 0.51 (d) What is the median checkout duration Ã? [solve 0.5 = F(Ñ)]. 3.5355 (e) Obtain the density function f(x). f(x) = F'(x) 1
Let X denote the amount of time a book on two-hour reserve is actually checked out, and suppose the cdf is the following. x < 0 x2 F(x) = 0 sx < 5 25 1 Use the cdf to obtain the following. (If necessary, round your answer to four decimal places.) (a) Calculate P(X < 3). 0.04 (b) Calculate P(2.5 s X s 3). -0.21 (c) Calculate P(X > 3.5). 0.51 (d) What is the median checkout duration Ã? [solve 0.5 = F(Ñ)]. 3.5355 (e) Obtain the density function f(x). f(x) = F'(x) 1
Let X denote the amount of time a book on two-hour reserve is actually checked out, and suppose the cdf is the following. x < 0 x2 F(x) = 0 sx < 5 25 1 Use the cdf to obtain the following. (If necessary, round your answer to four decimal places.) (a) Calculate P(X < 3). 0.04 (b) Calculate P(2.5 s X s 3). -0.21 (c) Calculate P(X > 3.5). 0.51 (d) What is the median checkout duration Ã? [solve 0.5 = F(Ñ)]. 3.5355 (e) Obtain the density function f(x). f(x) = F'(x) 1
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.)
(a)
Calculate P(X ≤ 3).
(b)
Calculate P(2.5 ≤ X ≤ 3).
(c)
Calculate P(X > 3.5).
(d)
What is the median checkout duration ? [solve 0.5 = F()].
(e)
Obtain the density functionf(x).
f(x)
=
F ′(x)
=
15x
0
≤
x < 5
0
otherwise
(f)
Calculate E(X).
(g)
Calculate V(X) and ?x.
V(X) ?x
(h)
If the borrower is charged an amount h(X) = X2 when checkout duration is X, compute the expected charge
E[h(X)].
Transcribed Image Text:Let X denote the amount of time a book on two-hour reserve is actually checked out, and suppose the cdf is the following.
x < 0
F(x) =
0 <x < 5
25
1
5 < x
Use the cdf to obtain the following. (If necessary, round your answer to four decimal places.)
(a) Calculate P(X < 3).
0.04
(b) Calculate P(2.5 < X < 3).
|-0.21
(c) Calculate P(X > 3.5).
0.51
(d) What is the median checkout duration i? [solve 0.5 = F()].
3.5355
(e) Obtain the density function f(x).
f(x) = F'(x)
1
0<x < 5
otherwise
(f) Calculate E(X).
8.3333
Transcribed Image Text:(e) Obtain the density function f(x).
f(x) = F'(x)
0 <x < 5
0.
otherwise
(f) Calculate E(X).
8.3333
(g) Calculate V(X) and oy.
V(X)
-64.4444
8.0277
(h) If the borrower is charged an amount h(X) = x2 when checkout duration is X, compute the expected charge E[h(X)].
Definition Definition Middle value of a data set. The median divides a data set into two halves, and it also called the 50th percentile. The median is much less affected by outliers and skewed data than the mean. If the number of elements in a dataset is odd, then the middlemost element of the data arranged in ascending or descending order is the median. If the number of elements in the dataset is even, the average of the two central elements of the arranged data is the median of the set. For example, if a dataset has five items—12, 13, 21, 27, 31—the median is the third item in ascending order, or 21. If a dataset has six items—12, 13, 21, 27, 31, 33—the median is the average of the third (21) and fourth (27) items. It is calculated as follows: (21 + 27) / 2 = 24.
Expert Solution
Step 1
Comment: As per the our company guidelines we are supposed to answer only three subparts. Kindly repost other parts in the next question.
Solution:
Let X denote the amount of time a book on two-hour reserve is actually checked out.
The cumulative distribution function (cdf) of X is
![Let X denote the amount of time a book on two-hour reserve is actually checked out, and suppose the cdf is the following.
x < 0
F(x) =
0 <x < 5
25
1
5 < x
Use the cdf to obtain the following. (If necessary, round your answer to four decimal places.)
(a) Calculate P(X < 3).
0.04
(b) Calculate P(2.5 < X < 3).
|-0.21
(c) Calculate P(X > 3.5).
0.51
(d) What is the median checkout duration i? [solve 0.5 = F()].
3.5355
(e) Obtain the density function f(x).
f(x) = F'(x)
1
0<x < 5
otherwise
(f) Calculate E(X).
8.3333](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8eaaea92-e247-4966-90e2-8af37fd7e5c3%2F04a5f591-1b68-43df-be52-888c85bb176a%2Fnizeqsg_processed.png&w=3840&q=75)
![(e) Obtain the density function f(x).
f(x) = F'(x)
0 <x < 5
0.
otherwise
(f) Calculate E(X).
8.3333
(g) Calculate V(X) and oy.
V(X)
-64.4444
8.0277
(h) If the borrower is charged an amount h(X) = x2 when checkout duration is X, compute the expected charge E[h(X)].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8eaaea92-e247-4966-90e2-8af37fd7e5c3%2F04a5f591-1b68-43df-be52-888c85bb176a%2F7w1pllr_processed.png&w=3840&q=75)
