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
RideAnS [48]
3 years ago
6

Define a new random variable by y = 2px. show that, as p l 0, the mgf of y converges to that of a chi squared random variable wi

th 2r degrees of freedom by showing that
Mathematics
1 answer:
Mandarinka [93]3 years ago
5 0
The moment generating function (mgf) of y is given by

M_y(t)=E(e^{ty})=E(e^{2pxt})=M_x(2pt)=p(1-e^{2pt}(1-p))^{-1}

Since the momoent generating function of x is given by M_x(t)=p(1-e^{t}(1-p))^{-1}

When p tends to 0, we have

\lim_{p \to 0} M_y(t)=  \lim_{p \to 0}  \frac{p}{1-e^{2pt}(1-p)} = \frac{0}{0}

Applying L'Hopital's rule we have:

\lim_{p \to 0} M_y(t)=\lim_{p \to 0} \frac{1}{e^{2pt}+2te^{2pt}+2pte^{2pt}} = \frac{1}{1+2t} , \ \ \ t\ \textless \  \frac{1}{2}

This shows that y converges to <span>a chi squared random variable with 2r degrees of freedom</span>.
You might be interested in
A 75.0 W bulb is connected to a
FromTheMoon [43]

Answer:

161

Step-by-step explanation: 110^2/75

8 0
3 years ago
An office supply store recently sold a black printer ink cartridge for $17.99 and a color printer ink cartridge for $20.99. At t
UNO [17]

Answer:

40 black ink cartridges and 19 colored ink cartridges

Step-by-step explanation:

Let b represent the number of black printer ink cartridges sold. Let c represent the number of color printer ink cartridges sold.

Set up a system of equations:

\displaystyle\\\begin{cases}b+c=59\\17.99b+20.99c=1,118.41\end{cases}

b+c=59\implies b=59-c

Substitute:

\displaystyle\\17.99(59-c)+20.99c=1,118.41\\\implies c=\boxed{19}

\implies b+19=59\implies b=\boxed{40}

⇒ 40 black ink cartridges, 19 colored ink cartridges (ans)

8 0
2 years ago
I have assessment quiz please
alekssr [168]

Answer:

A&B

....

...

....

.......

.....

7 0
2 years ago
Which of these is an example of the Commutative property of addition? And Explain why? 3+5=4+4 or 3+5=5+3
mestny [16]

Answer:

3+5=5+3

Step-by-step explanation:

Because the commutative property means 'flip-flop'

Hope this helps! = )

5 0
2 years ago
Read 2 more answers
A line segment is formed by connecting two points located at (-4,2) and (2,-1). What is the slope of this line segment? A.-3/8 B
Scorpion4ik [409]
The formula for slope is 
m= (y₂-y₁)/(x₂-x₁)
you can plug in the points that you are given to find the slope
m= (-1-2)/(2-(-4)
m= -3/6

the slope is -3/6 which reduced to -1/2

so the answer would be 
c) -1/2

hope this helped!
3 0
3 years ago
Other questions:
  • The ratio of 7th grade students to 8th grade students in a soccer league is 17:23. If there are 200 students in all, how many ar
    7·2 answers
  • The police department in Mansville employs 54 men and 36 women. What percent of the total are men? What is the answer to this qu
    6·2 answers
  • Describing each step.
    7·2 answers
  • How do you write 23.5 in word form
    6·2 answers
  • Find the measure of angle B.
    13·2 answers
  • John cut a paper square with a perimeter of 18 inches into two rectangles. The perimeter of one of the rectangles is 10 inches.
    12·2 answers
  • Which of the following is a true statement about functions ?
    15·1 answer
  • What is the slope of a line parallel to the line whose equation is 18x - 3y = -45 fully reduce your answer
    6·1 answer
  • Porfa es para un examen
    13·1 answer
  • What is the area of a parallelogram with a base of 7 meters and a height of 6 meters?
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!