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
Svetlanka [38]
3 years ago
11

(Uniform) Suppose X follows a continuous uniform distribution from 3 to 9. (a) Write down the PDF of X. (b) Find P(X ≤ 6). Round

your answer to 4 decimals. (c) Find P(4 < X ≤ 6). Round your answer to 4 decimals. (d) Determine the conditional probability P(X > 4 | X ≤ 6). Round your answer to 4 decimals
Mathematics
1 answer:
defon3 years ago
7 0

Answer:

a)  P(x) = {0.1667 for x in (3,9) ,   0 otherwise}

b) P(x≤6) = 0.5

c) P(4 < x ≤ 6) = 0.3333

d) P(X > 4 | X ≤ 6) = 0.3333 or 1 <em>*see below*</em>

<em />

Step-by-step explanation:

a)

Since it is a uniform distribution you can imagine it as a rectangle which extends from a = 3 to b = 9 and whose total area is 1.

Therefore the height must be equal to the inverse of the side:

P(X) = 1/(b-a) = 1/(9-3)= 1/6       for every x in (3,9)  and 0 otherwise

P(X) = 0.1667

b)

To find this probability we must find the area of the rectangle which extends from 3 to 6 and whose height is equal to P(x)

That is:

P(X ≤ 6) = (6-3)/(9-3) = 3/6 = 1/2 = 0.5

That make sense since 6 is half way between 3 and 9

c)

Similar to b) but now we consider tha base of the rectangle from 4 to 6:

P(4 < X ≤ 6) = (6-4)/(9-3) = 2/6 = 1/3 = 0.3333

d)

If  '' | '' means " or ", the probability is one, since every number in the range (3,9) is either higher than 4 or less than 6.

If " | " means " and " the answer is the same as in c , that is because 4<x≤6 is the set of numbers which are higher than 4 and at most 6 which can be expressed as x>4 and x≤6

You might be interested in
What is the radius of a sphere with a surface area of 144πcm2?
Bad White [126]

I believe the radius would be 3.39

Hope this helps! Good luck! :)

8 0
3 years ago
Read 2 more answers
A carpenter has a piece of wood that is 78 inches long. He wants to cut it so that one piece is five times as long as the other
Lyrx [107]

Answer:

13 and 65

Step-by-step explanation:

x + 5x = 78

(because u want a piece (x) and a piece that's five times longer than x- so 5x. and they should come from a 78 inch piece)

6x = 78

x = 78 / 6

x= 13

(to counter check:  13 * 5 = 65.  

                               65 + 13 = 78  )

7 0
3 years ago
Read 2 more answers
PLEase hurry please hURyy plaese hurry
steposvetlana [31]

<h2><u>PLEASE MARK BRAINLIEST!</u></h2>

Answer:

All these answers are correct. I triple - checked!

Step-by-step explanation:

In order from questions asked top - to - bottom:

First question:

  • 23 businesses

Second question:

  • 18 businesses

Third question:

  • 14 businesses

Fourth question:

  • 6 businesses

I hope this helps!

- sincerelynini

6 0
2 years ago
PLEASE HELP ME I REALLY NEED HELP PLEASEEEE If a circle has an area of 12πcm² and a diameter line AB, what is the length of arc
Softa [21]

Answer:

"Let's say it is equal to 45 degrees, or π/4. Calculate the arc length according to the formula above: L = r * Θ = 15 * π/4 = 11.78 cm . Calculate the area of a sector: A = r² * Θ / 2 = 15² * π/4 / 2 = 88.36 cm² . You can also use the arc length calculator to find the central angle or the radius of the circle. "

4 0
2 years ago
Chang made 6 identical necklaces each having beads and a pendant. The total cost of the beads and pendants for all 6 necklaces w
son4ous [18]

Answer:

One pendant costed $3.40

Step-by-step explanation:

6 0
2 years ago
Other questions:
  • FOR A TEST PLEASE ANSWER QUICK !!!
    6·1 answer
  • A Genesse High School, the Sophomore class has 60 more students than the Freshmen class. The junior class has 50 fewer students
    7·1 answer
  • How do u guys solve this problem
    12·2 answers
  •  In the first week of​ July, a record 1040 people went to the local swimming pool. In the second​ week, 110 fewer people went to
    5·1 answer
  • Two sides of a right triangle are 572 units long. What is the<br> perimeter of the triangle?
    15·1 answer
  • (this is multiple choice and i raised points make sure to EXPLAIN !)
    13·2 answers
  • Let g be the function given by g(x)=√ 1−sin2x. Which of the following statements could be false on the interval 0≤x≤π ?
    14·1 answer
  • Evaluate 4b-a when a=12 and b=7
    14·2 answers
  • If x−2/4=2, then x=10
    11·2 answers
  • At the state fair, admission at the gate is 10. In addition, the cost of each ride is 4. Suppose that Josh will go on x rides. J
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!