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
There are five boys and three girls in a swimming pool. If two people are selected at
Vlada [557]

Answer:

its a 3/8 chance that there are girls

Step-by-step explanation:

3 0
3 years ago
Can somebody answer this (on the picture) algebra question please
zheka24 [161]
I am torn between B and D because increased means add, but I am going to go with B 1 - 3n. I choose B because in the D option it decreases not increases. 

So the answer is B.) 1 - 3n
Hope this helps! - Alyssa

6 0
2 years ago
If a lap is 440 yard how many laps would need to be completed to run a mile
Nataly_w [17]
1760 yards = 1 mile

Therefore we divide 1760 / 440 = 4 laps to run to complete a mile.
4 0
3 years ago
Read 2 more answers
Select all the situations that can be represented by the tape diagram. 99 W W W W W 4 Clare buys 4 bouquets, each with the same
enot [183]

Answer:

Third one 33333333333333333

5 0
3 years ago
Read 2 more answers
I need help is it A B C Or D
Anarel [89]
Natural selection <span>is the process where organisms are more likely to reproduce. When they reproduce, they pass on traits to the next generation. Over time this process allows organisms to adapt to their environment. Giving what natural selection means, I believe the answer is D. Evolution does NOT always improve organisms. 

I hope this helps:)</span>
5 0
3 years ago
Other questions:
  • In how money ways can a five-letter license plate be made with the letters from April if none of the letters are repeated ?
    5·1 answer
  • The GCF of 28 and 64 is<br><br> 2<br> 4<br> 7<br> 8
    5·2 answers
  • Sunny earns $12 per hour delivering cakes. She worked for x hours this week. Unfortunately, she was charged $15 for a late deliv
    14·1 answer
  • Which expression is equal to 5x(m-n) <br> 1. (m-5)x(n-5)<br> 2. 5m-5n<br> 3. m-5n
    10·2 answers
  • Help!!! Please help me I need help on my homework!​
    7·1 answer
  • Find the value of x. (Type an integer or decimal.)
    14·1 answer
  • Someone help me please <br> whats the real cube root of -1 over 27
    11·1 answer
  • HELP MEEEEEEEEEEE I NEED HELPPPP
    12·1 answer
  • How much does Taryn charge to mow a lawn?
    8·2 answers
  • A recipe for dessert calls for 1/3 cup of powdered sugar and 2/6 cup of brown
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!