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
trasher [3.6K]
2 years ago
8

consider a sequence of independent tosses of a biased coin at times k=0,1,2,…,n. On each toss, the probability of Heads is p, an

d the probability of Tails is 1−p.A reward of one unit is given at time k, for k∈{1,2,…,n}, if the toss at time k resulted in Tails and the toss at time k−1 resulted in Heads. Otherwise, no reward is given at time k.Let R be the sum of the rewards collected at times 1,2,…,n.We will find E[R] and var(R) by carrying out a sequence of steps. Express your answers below in terms of p and/or n using standard notation. Remember to write '*' for all multiplications and to include parentheses where necessary.We first work towards finding E[R].1. Let Ik denote the reward (possibly 0) given at time k, for k∈{1,2,…,n}. Find E[Ik].E[Ik]=2. Using the answer to part 1, find E[R].E[R]=The variance calculation is more involved because the random variables I1,I2,…,In are not independent. We begin by computing the following values.3. If k∈{1,2,…,n}, thenE[I2k]=4. If k∈{1,2,…,n−1}, thenE[IkIk+1]=5. If k≥1, ℓ≥2, and k+ℓ≤n, thenE[IkIk+ℓ]=6. Using the results above, calculate the numerical value of var(R) assuming that p=3/4, n=10.var(R)=
Mathematics
1 answer:
omeli [17]2 years ago
5 0

Answer:

1. p*(1-p)

2. n*p*(1-p)

3. p*(1-p)

4. 0

5. p^2*(1-p)^2

6. 57/64

Step-by-step explanation:

1. Let Ik denote the reward (possibly 0) given at time k, for k∈{1,2,…,n}. Find E[Ik].

E[Ik]=  p*(1-p)

2. Using the answer to part 1, find E[R].

E[R]=  n*p*(1-p)

The variance calculation is more involved because the random variables I1,I2,…,In are not independent. We begin by computing the following values.

3. If k∈{1,2,…,n}, then

E[I2k]= p*(1-p)  

4. If k∈{1,2,…,n−1}, then

E[IkIk+1]=  0

5. If k≥1, ℓ≥2, and k+ℓ≤n, then

E[IkIk+ℓ]=  p^2*(1-p)^2

6. Using the results above, calculate the numerical value of var(R) assuming that p=3/4, n=10.

var(R)= 57/64

You might be interested in
Subtract -5x+7 from 3x-2 set up your expression show your work
ruslelena [56]

3x-2

-(-5x+7)

☝️this is your equation

distribute your subtraction sign to -5x+7 and you get

3x-2

+5x-7

add everything together and you end up with

8x-9

3 0
3 years ago
Read 2 more answers
Please help me ASAP
Natali5045456 [20]
2 units                                                                                                                                                   
........................................................................................
4 0
3 years ago
Read 2 more answers
A : 98<br> B : 31.1<br> C : 14 <br> D : 9.9<br><br><br> Please help :(
irina [24]

Hope you could understand.

If you have any query, feel free to ask.

4 0
2 years ago
A gram is 300 times smaller than kilogram true or false
tino4ka555 [31]
False it is 1,000 times smaller
4 0
2 years ago
Read 2 more answers
Given the side lengths, determine whether thr triangle is acute, right, ovtuse, or not a triangle:
DaniilM [7]

Answer:

1) If sum of the two smaller sides of a triangle is greater than the third longer side, then its a triangle.

<h3>In our case, 20 + 23 > 41. Hence its a triangle .</h3>

Use the side lengths to classify the triangle as acute, right, or obtuse. Compare the square of the length of the longest side with the sum of the squares of the lengths of the two shorter sides

2) Square root of sum of the squares of the two smaller sides is equal to the third longer side, then its a right triangle.

In our case,

√20^2+23^2≈30.4795<41.

<h3>Hence not a right triangle.</h3>

Since the sum of the squares of the two shorter sides is < the square of the longer side, its an obtuse angle triange

Step-by-step explanation:

Hope it is helpful....

6 0
2 years ago
Other questions:
  • What is the formal way to say add?
    8·2 answers
  • a horse trots in a circle at the end of a 4m rope. About how far does the horse trotted after completing ten circles?
    7·2 answers
  • An egg is dropped from a height of 90 ft. If acceleration due to gravity is -16 ft/s2 and initial velocity is Ofts, approximatel
    15·1 answer
  • Logan &amp; Billy scored a combined total of 90 points on a game. Logan scored 10 points more than Billy. How many points did Bi
    13·1 answer
  • Mandy obtains a $155,000 20/6 balloon mortgage with a rate of 4.25%. What will her monthly payments be?
    11·1 answer
  • 20. The perimeter of a square is 72 in. What is its area? 72 in2 324 in2 18 in2 5,184 in2
    13·1 answer
  • What is -31+-4x=-5+-5(1+5x)
    11·1 answer
  • Lacey filled a measuring cup with 1/2 of a cup of vegetable oil. Then she poured 1/3 of a cup of the oil into a frying pan. How
    8·1 answer
  • Solve.<br> 33 * (-81) =<br> -30<br> -24
    7·1 answer
  • Please HELP me I beg you!!!!!<br><br>NO LINKS!!!!!!!!<br><br>and THANK YOU.
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!