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
PLEASE I BEG OF U HELP - ill give brainliest
Inga [223]

Answer:

123 cm²

Step-by-step explanation:

You add the sum of all the faces in the shape

8 0
3 years ago
Read 2 more answers
Write a polynomial in factored form.
enyata [817]

Answer:

f(x)= x^3

Step-by-step explanation:

5 0
2 years ago
Answer -3(9+3)*2/2*2-(-2)
daser333 [38]

Answer:

-70

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
How do you write this in scientific notation?<br> 52 thousandths
wlad13 [49]

52 thousandths = 0.052

Move two decimal places to the right:

<h3><u>5.2 x 10⁻²   ⇒  the scientific notation</u></h3>
7 0
3 years ago
Read 2 more answers
Calculate the area of QRS
Eduardwww [97]

Answer:

  153 cm²

Step-by-step explanation:

The area is given by the formula ...

  A = (1/2)bh

where b is the base length, and h is the height measured perpendicular to the base.

The diagram shows b = QR = 18 cm, and h = 17 cm. So, the area is ...

  A = (1/2)(18 cm)(17 cm)

  A = 153 cm²

7 0
3 years ago
Other questions:
  • How much is a 15-percent down payment on a purchase price of $205,000?
    14·1 answer
  • 30 people want soda, how many 2 liter bottles do you you need so everyone but you have 300 ml glass's of soda?
    14·1 answer
  • I need to help my child do division but I don't know how to do it myself
    12·1 answer
  • Whats the word phrase of 2(5-n)
    15·1 answer
  • Simplify the expression (3k / 8)^2​
    13·1 answer
  • A customer pays an initial fee and a daily fee to rent a snowmobile. the total payment for 3 days is $92. the total payment for
    9·1 answer
  • Given:f(x)=x-7 and h(x)=2x+3 write the rule for f(h(x))
    10·1 answer
  • 1.
    9·1 answer
  • A square has a perimeter of 44yd. What is the length of each side?
    11·1 answer
  • 10.
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!