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
d1i1m1o1n [39]
2 years ago
11

Let X1, . . . ,Xn be an i.i.d. random sample from a N(0, 1) population. Define Y1 = 1 n n X i=1 Xi , Y2 = 1 n n X i=1 |Xi| . Cal

culate E(Y1) and E(Y2), and compare them.
Mathematics
1 answer:
nalin [4]2 years ago
8 0

For each 1\le i\le n, E[X_i]=0, so that

\displaystyle E[Y_1]=E\left[\frac1n\sum_{i=1}^nX_i\right]=\frac1n\sum_{i=1}^nE[X_i]=0

Meanwhile,

\displaystyle E[Y_2]=\frac1n\sum_{i=1}^nE[|X_i|]

Each of the X_i have PDF

f_{X_i}(x)=\dfrac1{\sqrt{2\pi}}e^{-x^2/2}

for x\in\Bbb R. From this we get

E[|X_i|]=\displaystyle\frac1{\sqrt{2\pi}}\int_{-\infty}^\infty|x|e^{-x^2/2}\,\mathrm dx=\sqrt{\frac2\pi}\int_0^\infty xe^{-x^2/2}\,\mathrm dx=\sqrt{\frac2\pi}

\implies E[Y_2]=n\sqrt{\dfrac2\pi}

You might be interested in
Please help with khan academy!
sergiy2304 [10]

Answer:

Let's imagine the image of the zoo.

The diameter is basically the length of the circle.

The penguin swam the radius.

To find the radius, we need to divide the diameter by 2.

The diameter is 20 meters.

20 \div 2 = 10 meters.

2 x pi x 10 = 62.83185307

62.83185307/2 = 31.41592654

Answer = 31.41592654

6 0
2 years ago
Read 2 more answers
If you don’t know the real answer don’t give me a fake one I just need help!
PtichkaEL [24]
Answer:
1. x + 24 = 3x
24 = 3x - x
24 = 2x
12 = x

3x
3 (12)
36

2. 10x - 27 = 7x
10x - 7x = 27
3x = 27
x = 9

7x
7 (9)
63

3. 5x + 1 = 6x - 13
5x - 6x = -13 - 1
-x = -14
x = 14

5x + 1
5 (14) + 1
71

4. 6x + 3 = 4x + 39
6x - 4x = 39 - 3
2x = 36
x = 18

6x + 3
6 (18) + 3
111

1. B
2. A
3. H
4. E

8 0
3 years ago
High school students across the nation compete in a financial capability challenge each year by taking a National Financial Capa
Nikolay [14]

Using the normal distribution, it is found that a student has to score 1.08 standard deviations above the mean to be publicly recognized.

<h3>Normal Probability Distribution</h3>

In a normal distribution with mean \mustandard deviation \sigmaz-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

  • It measures how many standard deviations the measure is from the mean.
  • After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.

The top 14% of the scores are given by scores above the 86th percentile, which corresponds to Z = 1.08, hence, a student has to score 1.08 standard deviations above the mean to be publicly recognized.

More can be learned about the normal distribution at brainly.com/question/24663213

4 0
2 years ago
This is my last question on my quiz i need help
IceJOKER [234]
What’s the question ?
8 0
2 years ago
Read 2 more answers
What number is 0.4% of 82.1?
STALIN [3.7K]
0.4% / 100 =0.004
0.004 x 82.1 = 0.3284
5 0
3 years ago
Other questions:
  • What base side length does the rectangular prism need to have the same volume??????
    8·1 answer
  • Need help with multiple answer math problem!
    7·1 answer
  • Leon read 5/7 of the pages in his book.He has 28 pages left to read.How many pages has he read already?
    9·1 answer
  • A field is a rectangle with a perimeter of 1300 feet. The length is 400 feet more than the width. Find the width and length of t
    8·1 answer
  • The standard size of a rectangular placemat is 14 inches by 16 inches. How much fabric is needed to make 6 standard placemats?
    10·2 answers
  • The length of a rectangle is 16m greater than the width. If the perimeter of a rectangle is 256m, what is the width of the recta
    9·1 answer
  • There are 363 students at Meadowbrook High School. There are 10 more
    15·1 answer
  • Use the distributive property to remove parentheses. <br> -8(x-3w-2)
    11·1 answer
  • I can't find a down arrow soo look at the image please!!
    14·2 answers
  • NOWW GOOD REWARDS AND BRAINLEST ANSWER ANY AND GET THE GOODS
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!