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
fomenos
3 years ago
12

Let U1, ..., Un be i.i.d. Unif(0, 1), and X = max(U1, ..., Un). What is the PDF of X? What is EX? Hint: Find the CDF of X first,

by translating the event X < x into an event involving U1,...,Un.
Mathematics
1 answer:
Kryger [21]3 years ago
6 0

Answer:

E(X)= n \int_{0}^1 x^n dx = n [\frac{1}{n+1}- \frac{0}{n+1}]=\frac{n}{n+1}

Step-by-step explanation:

A uniform distribution, "sometimes also known as a rectangular distribution, is a distribution that has constant probability".

We need to take in count that our random variable just take values between 0 and 1 since is uniform distribution (0,1). The maximum of the finite set of elements in (0,1) needs to be present in (0,1).

If we select a value x \in (0,1) we want this:

max(U_1, ....,U_n) \leq x

And we can express this like that:

u_i \leq x for each possible i

We assume that the random variable u_i are independent and P)U_i \leq x) =x from the definition of an uniform random variable between 0 and 1. So we can find the cumulative distribution like this:

P(X \leq x) = P(U_1 \leq 1, ...., U_n \leq x) \prod P(U_i \leq x) =\prod x = x^n

And then cumulative distribution would be expressed like this:

0, x \leq 0

x^n, x \in (0,1)

1, x \geq 1

For each value x\in (0,1) we can find the dendity function like this:

f_X (x) = \frac{d}{dx} F_X (x) = nx^{n-1}

So then we have the pdf defined, and given by:

f_X (x) = n x^{n-1} , x \in (0,1)  and 0 for other case

And now we can find the expected value for the random variable X like this:

E(X) =\int_{0}^1 s f_X (x) dx = \int_{0}^1 x n x^{n-1}

E(X)= n \int_{0}^1 x^n dx = n [\frac{1}{n+1}- \frac{0}{n+1}]=\frac{n}{n+1}

You might be interested in
20.Ju
Solnce55 [7]

Answer:

A  viable solution is the ordered pair (0,0)

Step-by-step explanation:

we know that

The number of books cannot be a negative number

The number of books is a positive integer

The weight cannot be a negative number

therefore

A  viable solution is the ordered pair (0,0)

4 0
3 years ago
Read 2 more answers
6a. In King County the sales tax is 9.5%. What is the total tax collected (tax ONLY) on a purchase of $222.00? I WILL GIVE YOU B
soldier1979 [14.2K]

Answer:

$

21.09

Step-by-step explanation:

7 0
3 years ago
Is 14/15 bigger than 4/5
liraira [26]

Answer:

Yes

Step-by-step explanation:

Multiply 4/5 so that they have a common denominator.

14/15 > 12/15 (4/5)

8 0
3 years ago
Read 2 more answers
What is the highest common factor of 60 and 75
Assoli18 [71]
<span>The factors of 60 are 60, 30, 20, 15, 12, 10, 6, 5, 4, 3, 2, 1.The factors of 75 are 75, 25, 15, 5, 3, 1.<span>The common factors of 60 and 75 are 15, 5, 3, 1, intersecting the two sets above.</span><span>In the intersection factors of 60 ∩ factors of 75 the greatest element is 15.</span><span>Therefore, the greatest common factor of 60 and 75 is 15.

</span></span>
8 0
3 years ago
A store salesperson is paid 3% of his sales as a commission. He made sales of $2500. How much was his commission?​
PolarNik [594]

1) Write 3% as 3/100

2) Since, finding the fraction of a number is same as multiplying the fraction with the number, we have:

\frac{3}{100} of 2500 = \frac{3}{100} × 2500

Therefore, the answer is 75

If you are using a calculator, simply enter 3÷100×2500 which will give you 75 as the answer.

Commission = $75

7 0
2 years ago
Other questions:
  • Which angle measure below is not a possible measure of an exterior angle of a regular polygon?
    10·1 answer
  • Lexi subtracts 9,405 from 11,138 should her answer be greater than or less than 2,000
    15·2 answers
  • F(n)=4n-3 find the 15th term of the sequence defined by the explicit rule
    13·1 answer
  • At Mario's Pizza, a large pizza has a diameter of 18 inches. What is the area of two pizzas?
    11·2 answers
  • Select the action you would use to solve 3x = 12. Then select the property
    9·1 answer
  • Lee and his friends ate 9/2 pizzas. How many pizzas is in mixed number forms
    6·1 answer
  • How to solve two step inequalities
    7·1 answer
  • Name 10 different rays. Then name 2 pairs of opposite rays. <br><br> I simply need to check answers!
    9·1 answer
  • The image shows a dust mite as seen under a microscope. The scale of the drawing to dust is 100:1
    11·1 answer
  • Which number line shows point M at 4/3
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!