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
Nostrana [21]
3 years ago
5

(Uniform) Suppose X follows a continuous uniform distribution from 4 to 11. (a) Write down the PDF of X. (b) Find P(X ≤ 7). Roun

d your answer to 4 decimals. (c) Find P(5 < X ≤ 7). Round your answer to 4 decimals. (d) Determine the conditional probability P(X > 5 | X ≤ 7). Round your answer to 4 decimals.
Mathematics
1 answer:
love history [14]3 years ago
7 0

Answer:

a) f(x)= \frac{1}{11-4}= \frac{1}{7}, 4 \leq x \leq 11

b) P(X\leq 7) = F(7) = \frac{7-4}{11-4}= 0.4286

c) P(5 < X \leq 7)= F(7) -F(5) = \frac{7-4}{7} -\frac{5-4}{7}= 0.2857

d) P(X >5 | X \leq 7)

And we can find this probability with this formula from the Bayes theorem:

P(X >5 | X \leq 7)= \frac{P(X>5 \cap X \leq 7)}{P(X \leq 7)}= \frac{P(5

Step-by-step explanation:

For this case we assume that the random variable X follows this distribution:

X \sim Unif (a=4, b =11)

Part a

The probability density function is given by the following expression:

f(x) = \frac{1}{b-a} , a \leq x \leq b

f(x)= \frac{1}{11-4}= \frac{1}{7}, 4 \leq x \leq 11

Part b

We want this probability:

P(X \leq 7)

And we can use the cumulative distribution function given by:

F(x) = \frac{x-a}{b-a}= \frac{x-4}{11-4}

And replacing we got:

P(X\leq 7) = F(7) = \frac{7-4}{11-4}= 0.4286

Part c

We want this probability:

P(5 < X \leq 7)

And we can use the CDF again and we have:

P(5 < X \leq 7)= F(7) -F(5) = \frac{7-4}{7} -\frac{5-4}{7}= 0.2857

Part d

We want this conditional probabilty:

P(X >5 | X \leq 7)

And we can find this probability with this formula from the Bayes theorem:

P(X >5 | X \leq 7)= \frac{P(X>5 \cap X \leq 7)}{P(X \leq 7)}= \frac{P(5

You might be interested in
Frederick needs to borrow $3000 for a down payment on a new car. His uncle decided to loan him the money as a 4.5% loan. Frederi
dolphi86 [110]
He has 6 years to pay back the loan.
8 0
3 years ago
Express the sum or difference as a product: cos 4x - cos 6x
Jobisdone [24]
Cos -2x or -cos2x, it's the difference.
3 0
3 years ago
Hey can you please help me posted picture of question
Elza [17]
Using the quadratic formula, the answers could be A B and D
5 0
3 years ago
Read 2 more answers
Find the Laplace Transform of the following function. <br><br> f(t) = 10 cos (12t+ 60°) u(t)
allsm [11]

Answer:

L(f(t)) = \frac{5s - 60\sqrt{3} }{s^2 + 144}

Step-by-step explanation:

f ( t ) = 10 cos ( 12t + 60°) u(t)

attached below is a detailed solution of the given problem

L(f(t)) = \frac{5s - 60\sqrt{3} }{s^2 + 144}

8 0
2 years ago
5x - Зу = 2<br> Find the slope of this equation
torisob [31]
The slope is 5/3 and the y- intercept is -2/3
8 0
3 years ago
Read 2 more answers
Other questions:
  • tom has 28 milk chocolates and emily has 24 dark chocolates they have to divide these chocolates into small packets that each ha
    12·2 answers
  • pe ling needs 2 yards of fabric for a craft project. she has 3 feet already.how many niches of fabric does she still need?
    6·1 answer
  • You are watching a commercial on television for the newest sandwich at ur favorite fast food chain.what type of promotion are u
    5·2 answers
  • It was once believed that all of the bodies of the solar system were perfect spheres with absolutely nothing on their surfaces.
    8·1 answer
  • What is y+x+z= Please help someone!!!!!
    15·2 answers
  • Plz help me this is mathswatch by the way
    12·2 answers
  • Choose the equation that represents the graph.
    9·1 answer
  • Help will mark brainliest
    8·1 answer
  • Identify the scale factor.
    5·2 answers
  • Pwease help me with math question pwease
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!