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
Musya8 [376]
2 years ago
10

Suppose that the length of a side of a cube X is uniformly distributed in the interval 9

Mathematics
1 answer:
Nastasia [14]2 years ago
8 0

Answer:

f(v) = \left \{ {{\frac{1}{3}v^{-\frac{2}{3}}\ 9^3 \le v \le 10^3} \atop {0, elsewhere}} \right.

Step-by-step explanation:

Given

9 < x < 10 --- interval

Required

The probability density of the volume of the cube

The volume of a cube is:

v = x^3

For a uniform distribution, we have:

x \to U(a,b)

and

f(x) = \left \{ {{\frac{1}{b-a}\ a \le x \le b} \atop {0\ elsewhere}} \right.

9 < x < 10 implies that:

(a,b) = (9,10)

So, we have:

f(x) = \left \{ {{\frac{1}{10-9}\ 9 \le x \le 10} \atop {0\ elsewhere}} \right.

Solve

f(x) = \left \{ {{\frac{1}{1}\ 9 \le x \le 10} \atop {0\ elsewhere}} \right.

f(x) = \left \{ {{1\ 9 \le x \le 10} \atop {0\ elsewhere}} \right.

Recall that:

v = x^3

Make x the subject

x = v^\frac{1}{3}

So, the cumulative density is:

F(x) = P(x < v^\frac{1}{3})

f(x) = \left \{ {{1\ 9 \le x \le 10} \atop {0\ elsewhere}} \right. becomes

f(x) = \left \{ {{1\ 9 \le x \le v^\frac{1}{3} - 9} \atop {0\ elsewhere}} \right.

The CDF is:

F(x) = \int\limits^{v^\frac{1}{3}}_9 1\  dx

Integrate

F(x) = [v]\limits^{v^\frac{1}{3}}_9

Expand

F(x) = v^\frac{1}{3} - 9

The density function of the volume F(v) is:

F(v) = F'(x)

Differentiate F(x) to give:

F(x) = v^\frac{1}{3} - 9

F'(x) = \frac{1}{3}v^{\frac{1}{3}-1}

F'(x) = \frac{1}{3}v^{-\frac{2}{3}}

F(v) = \frac{1}{3}v^{-\frac{2}{3}}

So:

f(v) = \left \{ {{\frac{1}{3}v^{-\frac{2}{3}}\ 9^3 \le v \le 10^3} \atop {0, elsewhere}} \right.

You might be interested in
Which expression represent, 3 times the sum of 7 and m.
Marina CMI [18]
D would be the answer.Since you are adding the sum first hence the parentheses.
5 0
3 years ago
What’s the answer to this
jeyben [28]
It is somewhere in between 7,4 and 4,8
5 0
3 years ago
Write each verbal expression as an algebraic expression.
weeeeeb [17]

Answer:

6(d-5)

Step-by-step explanation:

i think this must be the equation

4 0
3 years ago
Based on the graph, which statements about the points could be true? Check all that apply.
aliina [53]

Answer:

A. Point D could be the image of B.

D is up and to the right of B, so yes. Select choice A

B. Point C could be the image of A.

C is below A, so no

C. Point E could be the image of C.

E is up and to the right from C so yes, Select choice C

D. Point D could be the image of A.

D is down and to the right of A so no.

E. Point E could be the image of B.

E is up and to the right of B so yes. Select choice E

F. Point C could be the image of E.

No C is down and to the left of E.

Answers: A C E

Step-by-step explanation:

3 0
3 years ago
Rewrite 4/7 and 3/5 so they have common denominator
Vladimir [108]
20/35 and 21/35. The common denominator is 35.
6 0
3 years ago
Other questions:
  • You start an account with $500 and an interest rate of 6% compounded yearly. How much is in the account after 3 years?
    9·1 answer
  • If the y-intercept is b= -9 and the slope is m= 1. What is the slope intercept form? How do I set it up?
    10·1 answer
  • Madvi was playing a card game with her friends. Each time she played Madvi Lost 13 points. If Madvi played 5 rounds, how many po
    12·1 answer
  • 34699 to nearest ten thousand
    8·1 answer
  • Please Help Me
    5·1 answer
  • What are 4 equivalent fractions for 1/4
    14·2 answers
  • Mixed problem with fractions <br> 1 over 2 minus 1 over 4
    13·1 answer
  • Please rate them need to know which one to put as profile pic
    13·1 answer
  • Can someone give me a fake band name???
    11·1 answer
  • Olivia saves $15 each week and has $20 in an
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!