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-BARSIC- [3]
2 years ago
12

The steps to solve this problem

Mathematics
1 answer:
Free_Kalibri [48]2 years ago
4 0
I can't see an imagine I'm really sprry
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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,
Kryger [21]

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}

6 0
3 years ago
Help w graph proportional relationships questions!
stiv31 [10]
You're welcome! This took me forever!

6 0
2 years ago
What is 56/1/3 = ?beats per minute
alisha [4.7K]

Answer: i hope im right

between 60 and 100 beats per minute (bpm). A resting heart rate slower than 60 bpm is considered bradycardia.May 7, 2018

Step-by-step explanation:

7 0
2 years ago
PLEASE HELP! GIVING POINTS :)!
Stells [14]

Answer:

8 23/40

Step-by-step explanation:

8 and 5 have 40 in common. To get from 8 to 40 you need to multiply by 5. You have to do the same to the top and bottom numbers in the fraction. 3/8 turns into 15/40. To get from 5 to 40, you need to multiply by 8. Again, u have to do the same for the top and bottom. 1/5 turns into 8/40. 15/40 + 8/40 = 23/40. Add the whole numbers, 6 and 2, to get 8. So the answer in 8 23/40. Hope this helps!

5 0
2 years ago
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Maggie has been exercising by climbing steps. Her climbing rate at the end of week 1 was 25 steps per minute. At the end of week
UNO [17]

Answer:

60%

Step-by-step: the percent increase in Maggie's rate of climbing steps from the end of week 1 to the end of week 4 = 60%

7 0
2 years ago
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