1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
geniusboy [140]
3 years ago
14

11. Let X denote the amount of time a book on two-hour reserve is actually checked out, and suppose the cdf is F(x) 5 5 0 x , 0

x2 4 0 # x , 2 1 2 # x a. Calculate P(X # 1). b. Calculate P(.5 # X # 1). c. Calculate P(X . 1.5). d. What is the median checkout duration m ,? [solve .5 5 F(m ,)]. e. Obtain the density function f (x). f. Calculate E(X).
Mathematics
1 answer:
NISA [10]3 years ago
4 0

Question not properly presented

Let X denote the amount of time a book on two-hour reserve is actually checked out, and suppose the cdf is F(x)

0 ------ x<0

x²/25 ---- 0 ≤ x ≤ 5

1 ----- 5 ≤ x

Use the cdf to obtain the following.

(a) Calculate P(X ≤ 4).

(b) Calculate P(3.5 ≤ X ≤ 4).

(c) Calculate P(X > 4.5)

(d) What is the median checkout duration, μ?

e. Obtain the density function f (x).

f. Calculate E(X).

Answer:

a. P(X ≤ 4) = 16/25

b. P(3.5 ≤ X ≤ 4) = 3.75/25

c. P(4.5 ≤ X ≤ 5) = 4.75/25

d. μ = 3.5

e. f(x) = 2x/25 for 0≤x≤2/5

f. E(x) = 16/9375

Step-by-step explanation:

a. Calculate P(X ≤ 4).

Given that the cdf, F(x) = x²/25 for 0 ≤ x ≤ 5

So, we have

P(X ≤ 4) = F(x) {0,4}

P(X ≤ 4) = x²/25 {0,4}

P(X ≤ 4) = 4²/25

P(X ≤ 4) = 16/25

b. Calculate P(3.5 ≤ X ≤ 4).

Given that the cdf, F(x) = x²/25 for 0 ≤ x ≤ 5

So, we have

P(3.5 ≤ X ≤ 4) = F(x) {3.5,4}

P(3.5 ≤ X ≤ 4) = x²/25 {3.5,4}

P(3.5 ≤ X ≤ 4) = 4²/25 - 3.5²/25

P(3.5 ≤ X ≤ 4) = 16/25 - 12.25/25

P(3.5 ≤ X ≤ 4) = 3.75/25

(c) Calculate P(X > 4.5).

Given that the cdf, F(x) = x²/25 for 0 ≤ x ≤ 5

So, we have

P(4.5 ≤ X ≤ 5) = F(x) {4.5,5}

P(4.5 ≤ X ≤ 5) = x²/25 {4.5,5}

P(4.5 ≤ X ≤ 5)) = 5²/25 - 4.5²/25

P(4.5 ≤ X ≤ 5) = 25/25 - 20.25/25

P(4.5 ≤ X ≤ 5) = 4.75/25

(d) What is the median checkout duration, μ?

Median is calculated as follows;

∫f(x) dx {-∝,μ} = ½

This implies

F(x) {-∝,μ} = ½

where F(x) = x²/25 for 0 ≤ x ≤ 5

F(x) {-∝,μ} = ½ becomes

x²/25 {0,μ} = ½

μ² = ½ * 25

μ² = 12.5

μ = √12.5

μ = 3.5

e. Calculating density function f (x).

If F(x) = ∫f(x) dx

Then f(x) = d/dx (F(x))

where F(x) = x²/25 for 0 ≤ x ≤ 5

f(x) = d/dx(x²/25)

f(x) = 2x/25

When

F(x) = 0, f(x) = 2(0)/25 = 0

When

F(x) = 5, f(x) = 2(5)/25 = 2/5

f(x) = 2x/25 for 0≤x≤2/5

f. Calculating E(X).

E(x) = ∫xf(x) dx, 0,2/5

E(x) = ∫x * 2x/25 dx, 0,2/5

E(x) = 2∫x ²/25 dx, 0,2/5

E(x) = 2x³/75 , 0,2/5

E(x) = 2(2/5)³/75

E(x) = 16/9375

You might be interested in
Find the area of a triangle whose sides are 3cm,6cm and 7cm
nadya68 [22]

Answer:

See below

Step-by-step explanation:

It is NOT  a RIGHT triangle so you <u>cannot use</u>   1/2 b * h

 but you can use Heron's Formula

Area = sqrt( s (s-a)(s-b)(s-c) )

s = semi- perimeter =   (3+6+7)/2 = 8

Area = sqrt ( 8 ( 8-3)(8-6)(8-7) )   = sqrt ( 80) = 8.9 cm^2

4 0
1 year ago
What is the number of possible outcomes when a coin is tossed one time
Salsk061 [2.6K]

Answer:

2.

Step-by-step explanation:

the coin could be heads or tails, but knowing me prolly 3 because I would lose the coin when I flip it.

6 0
3 years ago
Read 2 more answers
PLEASE HELP ITS URGENT
OlgaM077 [116]

The missing step in this proof is ∠BAC ≅ ∠BDE ⇒ answer D

Step-by-step explanation:

If two triangles are similar by SAS, then their corresponding angles are

equal and the 3rd corresponding sides have constant ratio

In the two triangles ABC and DBE:

  • ∠ABC ≅ ∠DBE
  • \frac{AB}{DB}=\frac{BC}{BE}

Then the two triangles are similar

From similarity:

∠BAC ≅ ∠BDE

∠BCA ≅ ∠BED

∴ The missing step is ∠BAC ≅ ∠BDE

The missing step in this proof is ∠BAC ≅ ∠BDE

Learn more:

You can learn more about triangles in brainly.com/question/3451297

#LearnwithBrainly

8 0
3 years ago
Read 2 more answers
What is 83 divided by 3
Ksivusya [100]
83 divided by 3. 
Exact Form: 83/3
Decimal Form: 27.66666666. . .
Mixed Number Form: 27 2/3
4 0
3 years ago
Answer asap please!!
skad [1K]
Answer is B. 11. The square root is roughly 10.5, so you round up and get 11
5 0
3 years ago
Other questions:
  • How much does 7 3/4 yd of silk ribbon cost if 4/5 yd costs $5.60?
    10·1 answer
  • How do you do 16-19?
    5·2 answers
  • Find the value of x . round the nearest hundredth . <br><br>A.12.37<br>B.7.51<br>C.10.63<br>D.9.79
    13·1 answer
  • Roger can shovel his family's driveway in 1 hour. His older sister, Alexis, can shovel the driveway in 1/2 hour. If they work to
    9·2 answers
  • What is 4/7 multiplied by 13/9
    14·1 answer
  • Micah has a loan of $6,720. This loan has a simple interest rate of 3.5% per year. What is the amount of interest that Micah wil
    6·1 answer
  • If a linear regression has a correlation coefficient of 0.85, which of the following statements is true?
    9·2 answers
  • Sam and Liam raced each other up and then down the hill. Sam's average speed up the hill was 1 mph, and his average speed down w
    11·1 answer
  • Solve for X<br> 50 points in it for you plus a thanks, 5 star rating and brainliest!
    6·2 answers
  • Can someone help please? u dont have to show work so dont mind that
    14·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!