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
Ludmilka [50]
3 years ago
13

For each of the following sequences, determine whether it converges in probability to a constant. If it does, enter the value of

the limit. If it does not, enter the number "999".
1) Let X1,X2,… be independent continuous random variables, each uniformly distributed between −1 and 1.
a) Let Ui=X1+X2+⋯+Xii, i=1,2,…. What value does the sequence Ui converge to in probability? (If it does not converge, enter the number "999". Similarly in all below.)
b) Let Σi=X1+X2+⋯+Xi, i=1,2,…. What value does the sequence Σi converge to in probability?
c) Let Ii=1 if Xi≥1/2, and Ii=0, otherwise. Define,
Si=I1+I2+⋯+Iii.
What value does the sequence Si converge to, in probability?
d) Let Wi=max{X1,…,Xi}, i=1,2,…. What value does the sequence Wi converge to in probability?
e) Let Vi=X1⋅X2⋯Xi, i=1,2,…. What value does the sequence Vi converge to in probability?
2) Let X1,X2,…, be independent identically distributed random variables with E[Xi]=2 and Var(Xi)=9, and let Yi=Xi/2i.
a) What value does the sequence Yi converge to in probability?
b) Let An=1n∑i=1nYi. What value does the sequence An converge to in probability?
c) Let Zi=13Xi+23Xi+1 for i=1,2,…, and let Mn=1n∑i=1nZi for n=1,2,…. What value does the sequence Mn converge to in probability?

Mathematics
1 answer:
nikklg [1K]3 years ago
6 0

Answer:

Check the explanation

Step-by-step explanation:

Kindly check the attached images below for the step by step explanation to the question above.

You might be interested in
TRUE or FALSE: Every number raised to a negative exponent will have a value smaller than 1. Explain your reasoning.
Sveta_85 [38]

Answer:

<h3><u>Required Answer</u><u>:</u><u>-</u></h3>

Every number raised to a negative exponent will have a value smaller than 1.

  • This is False statement
<h3><u>Reason</u><u> </u><u>:</u><u>-</u></h3>
  • It will only be negative if the number is negative with an odd exponent.
  • what you're actually doing is dividing instead of multiplying.
<h3>For Example:-</h3>

\sf 4^2=16 \\ But \\ \sf 4^{-2}={\dfrac {1}{16}}

5 0
3 years ago
There was 4/5 of a cake sitting on the counter. Daryl ate 1/3 of the left over cake. How much cake was left over after he ate? *
bulgar [2K]

Answer:

<h3>                \bold{\dfrac8{15}}  of the cake       </h3>

Step-by-step explanation:

\dfrac45-\dfrac13\cdot\dfrac45=\dfrac{4\cdot3}{5\cdot3}-\dfrac4{15}=\dfrac{12}{15}-\dfrac4{15}=\dfrac8{15}

5 0
3 years ago
Read 2 more answers
17. Find the perimeter of a circle that is 10cm in diameter.
dimaraw [331]

Step-by-step explanation:

I think the answer is (a) hope this helps

4 0
2 years ago
Read 2 more answers
Choose the equation that represents the line passing through the point (-3,-1) with a slope of 4.
insens350 [35]
The answer would be c
5 0
3 years ago
Read 2 more answers
Number 9 help brainliest
Solnce55 [7]

Answer:

31 1/2 inches on the map

Step-by-step explanation:

The scale is 1.5 inches to 4 miles

He went 84 miles

We can use proportions to solve

1.5 inches        x inches

----------------- = ------------

4 miles               84 miles

Using cross products

1.5 * 84 = 4x

126 = 4x

Divide by 4

126/4 = 4x/4

31.5 =x

31 1/2 inches on the map

7 0
3 years ago
Other questions:
  • Julie went to the store with $20.00. if she bought 8 cans of dog food for $.67 per can, how much money did she have left? IF YOU
    14·2 answers
  • Question 1 WRONG With what number must 3.475817 be multiplied in order to obtain the number 34,758.17? A 100 1,000 10,000 D 100,
    14·1 answer
  • PLEASE HELP. I AM TRULY STUMPED.
    12·1 answer
  • What is the domain and range of the exponential function?
    10·1 answer
  • 2350 million in standard form
    5·2 answers
  • What's number 2 and 3
    5·1 answer
  • Given the table, Write the equation of the line
    6·1 answer
  • 1. Simplify:<br>4(4y-7y^{2})-9(5y+2)<br><br>2. Simplify:<br>24 – 4(5y – 6z) + 3y – 7z
    9·1 answer
  • 7x+9y=-41 and x+3y=1. Solve system of equations
    9·1 answer
  • 10A. A triangle has side lengths of 10 centimeters, 24 centimeters and 28
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!