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
dusya [7]
2 years ago
8

Mathematical Statistics with Applications Homework Help

Mathematics
1 answer:
photoshop1234 [79]2 years ago
4 0

7.37:

a. <em>W</em> follows a chi-squared distribution with 5 degrees of freedom. See theorem 7.2 from the same chapter, which says

\displaystyle \sum_{i=1}^n\left(\frac{Y_i-\mu}{\sigma}\right)^2

is chi-squared distributed with <em>n</em> d.f.. Here we have \mu=0 and \sigma=1.

b. <em>U</em> follows a chi-squared distribution with 4 degrees of freedom. See theorem 7.3:

\displaystyle \frac1{\sigma^2}\sum_{i=1}^n (Y_i-\overline Y)^2

is chi-squared distributed with <em>n</em> - 1 d.f..

c. <em>Y₆</em>² is chi-square distributed for the same reason as <em>W</em>, but with d.f. = 1. The sum of chi-squared distributed random variables is itself chi-squared distributed, with d.f. equal to the sum of the individual random variables' d.f.s. Then <em>U</em> + <em>Y₆</em>² is chi-squared distributed with 5 + 1 = 6 degrees of freedom.

7.38:

a. Notice that

\dfrac{\sqrt 5 Y_6}{\sqrt W} = \dfrac{Y_6}{\sqrt{\frac W5}}

and see definition 7.2 for the <em>t</em> distribution. Since <em>Y₆</em> is normally distributed with mean 0 and s.d. 1, it follows that this random variable is <em>t</em> distributed with 5 degrees of freedom.

b. Similar manipulation gives

\dfrac{2Y_6}{\sqrt U} = \dfrac{\sqrt4 Y_6}{\sqrt U} = \dfrac{Y_6}{\sqrt{\frac U4}}

so this r.v. is <em>t</em> distributed with 4 degrees of freedom.

You might be interested in
What is 3 copies of 1/3
jarptica [38.1K]

Answer: 1

Step-by-step explanation:

3 copies of 1/3 would be 1/3+1/3+1/3= 1

6 0
3 years ago
Shara collected two different data sets and label them dataset S and data said T.
Kamila [148]

Answer:

What are you asking?

Step-by-step explanation:

4 0
3 years ago
How do I figure this anser-6w &lt; 84​
Sophie [7]

Answer:

w > -14

Step-by-step explanation:

Divide both sides by -6.

-6w/-6 = w

84/-6 = 14

Since it's an equality, if the coefficient of the variable is negative, when you divide the sign flips to the opposite.

4 0
3 years ago
Which statement best applies to the slope of the line
Anastaziya [24]
Rise over run change in y/change in x
6 0
3 years ago
PLEASE HELP!!! i will give you brainly!
jenyasd209 [6]

Answer:

-96

Step-by-step explanation:

15+11=26+7=33+(-129)=-96

6 0
2 years ago
Read 2 more answers
Other questions:
  • I need to make sure this is correct .. thankyou
    12·1 answer
  • Need help with as many possible
    7·1 answer
  • Using the polygon angle sum theorem, find x in the graphic above
    14·1 answer
  • Three ounces of cinnamon cost $2.40. If there are 16 ounces in 1 pound, how much does cinnamon cost per pound?
    9·1 answer
  • Line segment ON is perpendicular to line segment ML.
    12·1 answer
  • A local fun raiser collected 525$ for a local children's hostpital one person donated 45$ and the donated 75$ the rest of the mo
    11·1 answer
  • PLEASE HELP ME I WILL GIVE BRAINLIEST
    15·2 answers
  • Helppppppppppppppppppppp
    5·1 answer
  • I don't understand..i just learned this but the teacher told us to study by ourselves please help ​
    15·1 answer
  • A batting average in baseball is calcite by dividing the number of timesavers player hits the ball by the number of times the pl
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!