You have a coin with unknown probability p of coming up heads. You wish to generate a random variable which takes the values 0 and 1, each with probability 1/2. Assume 0 < p < 1. You adopt the following procedure. You start by flipping the coin twice. If both flips produce the same side of the coin, you start again. If the result of the first flip is different from the result of the second flip, you report the result of the first flip, and you are finished (this is a trick originally due to John von Neumann). (a) Show that, in this case, the probability of reporting heads is 1/2. (b) What is the expected number of flips you must make before you report a result?

Answers

Answer 1

Answer:

(a) Hence, the probability of reporting heads is 1/2.

(b) Therefore, the expected number of such trial is 1 / 2p (1 –p).

Step-by-step explanation:

Solution:

To generate a random variable takes value 0 and 1.

Let 0 < p <1,

A coin is flipped twice.

(a) Probability of reporting head is 1/2.

The result of two toss is either HT or TH.

In this case we used conditional property, Given that you got either HT or TH,

Probability of occurring head or tail:

P (1ST = H| HT or TH]

= P (H) / P (HT or TH)

= P (HT) / P (HT or TH)

= P (1-P) / P (1-P) + (1-P)P

= P (1-P) / 2P (1-P)

=1/2

Hence, the probability of reporting heads is 1/2.

(b) Expected number of flip before report a result.

The probability of reporting a result on each trial is:

P (HT or TH)

=P (HT) + P (TH)

=P (1-P) + (1 –P) P

= 2P (1 –P)

Since, E(X) = 1 / P

Therefore, the expected number of such trial is 1 / 2p (1 –p).


Related Questions

In Ms. Renault's classroom, 2/5 of the students play sudoku. Of the student who play sudoku, 5/6 also play checkers. If there are 30 students in her class, how many play sudoku and checkers?

Answers

Answer:

10 students play sudoku and checkers

Step-by-step explanation:

First find the number of students that play sudoku

2/5 * 30

12

of those 12 students, 5/6 play checkers

12 * 5/6 = 10

10 students play sudoku and checkers

What do you think the important skills necessary in solving problems in differential calculus?

Answers

Answer:

idk if this helps but here:

Cutoff points are a crucial piece of calculus and are among the main things that understudies find out about in a calculus class. So, finding the constraint of a capacity implies figuring out what esteem the capacity approaches as it draws nearer and more like a specific point.

Step-by-step explanation:

the graph shows the total number of inches of snow that fell in a town in february over ten year period. what is the approximate probability that year 11 will have more that 15 inches of snow?

Answers

Answer:

0.6 because its 58% chance which is 0.58 which rounds to 0.6

Step-by-step explanation:

A TV show has 26 episodes. Due to the lack of time, you can onlywatch 5 of them. However, in order to get a gist of what the showis about, you do not want to watch any two consecutive episodes.How many selections of 5 episodes are there with no two consecutiveepisodes chosen? Assuming that the order of selection is irrelevant.(Hint:this is a Stars and Bars problem)

Answers

Answer:

Step-by-step explanation:

Recall that: The number of combination to select any k consecutive element from n consecutive term is given by the equation [tex]^{n-k+1}C_k[/tex]

[tex]= \begin {pmatrix} ^{n-k+1}_{k} \end {pmatrix}[/tex]

where:

n = 26

k = 5

[tex]^{n-k+1}C_k= \begin {pmatrix} ^{26-5+1}_{5} \end {pmatrix}[/tex]

[tex]^{n-k+1}C_k= \begin {pmatrix} ^{22}_{5} \end {pmatrix}[/tex]

[tex]^{n-k+1}C_k= \dfrac{22!}{5!(22-5)!}[/tex]

[tex]^{n-k+1}C_k= \dfrac{22!}{5!(17)!}[/tex]

[tex]\mathbf{^{n-k+1}C_k=26334}[/tex]

Therefore, there are 26334 selection of 5 episodes with no two consecutive episodes chosen

Please help answer this for me :)

Answers

Answer:

d=3/2 this should be it

Step-by-step explanation:

AMY HAS TWO TOMATO PLANTS. ONE IS 5 3/4 INCHES TALL AND THE OTHER IS 8 1/2 INCHES TALL. WHAT IS THE DIFFERENCE IN HEIGHT BETWEEN THE TWO TOMATO PLANTS?

Answers

The answer is 2 3/4 inches

Simplify the given expressions.

(7−2)2−(2+1)(2−5)

Answers

Answers 19 hope it helps you :)!

The answer is 19. ( i think)

USE A PROTRACTOR TO MEASURE THE FOLLOW
1)
2)
Answer:
Answer:
3)
4)

Answers

Answer:

1) 130°

2) 180°

3) 200°

4) 50°

Step-by-step explanation:

Hope it helps!!

:D

HELP ASAP PLEASE!!!!!!!!

Answers

Answer:

b) in the fourth round, there was one team left in the tournament.

c) no because with only one team left, the tournament ends.

Line segment YZ was used to translate A B CDE. YZ is 6.9 inches long. What is the length of
A A ' + B B ' + C C ' + DD' + E E '?
The length of A A ' + B B ' + C C ' + DD' + E E ' is inches.

Answers

Answer:

34.5

Step-by-step explanation:

you are adding 6.9 together , or 6.9 x 5 = 34.5

When Alexander moved into a new house, he planted two trees in his backyard. At

the time of planting, Tree A was 36 inches tall and Tree B was 21 inches tall. Each

year thereafter, Tree A grew by 6 inches per year and Tree B grew by 9 inches per

year. Let A represent the height of Tree At years after being planted and let B

represent the height of Tree Bt years after being planted. Write an equation for each

situation, in terms of t, and determine which tree is taller after 3 years.

Answers

Answer:

The equations for each situation are

A = 36 + 6t

B = 21 + 9t

After 3 years, Tree A is taller.

Step-by-step explanation:

From the question,

Tree A was 36 inches tall and Tree B was 21 inches tall at the time of planting; and

Tree A grew by 6 inches per year and Tree B grew by 9 inches per  year after planting.

For Tree A,

Given a period of t years after planting, the height would have increased by 6t

A = 36 + 6t

For Tree B,

Given a period of t years after planting, the height would have increased by 9t

B = 21 + 9t

To determine, which tree is taller after 3 years,

t = 3

For Tree A

A = 36 + 6t

A = 36 + 6(3)

A = 36 + 18

A = 54 inches

For Tree B

B = 21 + 9t

B = 21 + 9(3)

B = 21 + 27

B = 48 inches

Hence, After 3 years, Tree A is taller.

18 rolls of paper towels cost $25.99. Determine the cost of one roll of
toilet paper.

Answers

Answer:

$1.44

Step-by-step explanation:

Answer:

$1.44

Step-by-step explanation:

You divide $25.99 by 18 to get $1.44

Which of the following is the equivalent to the ratio 5:37
A 10:8
B 20:15
15:9
D 4:2

Answers

Answer:

Step-by-step explanation:

U would 22999+122.3939ading j. Till u wil go to the bathroom

Rewrite the following using the GCF and the distributive property
:32 + 54

Answers

Answer:

GCF: 2

Step-by-step explanation:

GCF: 2

(2*16) + (2*27)

What’s the slope of (-8,2) (1,9)

Answers

Step-by-step explanation:

equation of the line passing through two points

x-x1/x2-x1=y-y1/y2-y1

x-(-8)/1-(-8)=y-2/9-2

x+8/9=y-2/7

7x+56=9y-18

9y=7x+56+18

y=7/9x+74/9

y=mx+b m is the slope

so m=7/9

there is a short way showing slope shown in the picture

-12.5 - (-4.8) What is the value of the expression?

Answers

When you are determining the answer to the question, make sure you know to change the signs. The answer is - 7. 7

Raj and his friends went to the movies today and ate 875 Which steps can be used to find how much popcorn pieces of popcorn, or 125% more than they ate when Raj and his friends ate at the movies last week? they went to the movies last week. Check all that apply. Popcorn 125 + 750 = 875 eaten today 0 125 875 O 125 x 7 = 875 100 x 7 = 700 pieces of popcorn 100 + 750 = 850 pieces of popcorn 0 100 ? 125 + 875 = 1000 pieces of popcorn Popcorn eaten last week​

Answers

Answer:

125 x 7 = 875 pieces of popcorn

100 x 7 = 700 pieces

Step-by-step explanation:

Answer:

Step-by-step explanation:

B and C

I need help on this I will give brainlist help it will mean a lot this is my last math problem help me!​

Answers

Answer:

the second one

Step-by-step explanation:

i did it in my head and double checked :)

Answer:

Store Z has the best sale price of $28

Step-by-step explanation:

Starting Price = $35

Store X offers 15% off = only 5.25$ off (0.15 * 35 = 5.25, 35 - 5.25 = 29.75) Final Price = $29.75

Store Y offers $5 off = only 5$ off (35 - 5 = 30) Finaly Price = $30

Store Z offers 1/5 off = only 7$ off (1/5 = 0.20, 0.20 * 35 = 7, 35 - 7 = 28) Final Price = $28 (BEST PRICE)

A. <5, <7, <8, <11, <12, <14, <16, <17

B. <7,<8,<11,<12,<15,<16,<17,<18

C. <7,<8,<11,<12,<16,<17

D. <11, <12

Answers

Answer:im going to play roblox

Step-by-step explanation:

working through this one. An airplane cuts through the morning sky. For every 1,000 feet that it climbs, the outside temperature drops 20 degrees Fahrenheit What is the rate of temperature change in degrees Fahrenheit per foot? In the following activity, you'll use what you know about dividing rational numbers to find the solution. Complete the steps below to answer the question. write the change in elevation and the temperature as rational number.​

Answers

Answer:

1 degree per 50 ft

Step-by-step explanation:

1000÷20 = 50

each square below represents one whole​

Answers

Answer:

hello…

the colored part is 20%

The shaded part should be equal to 175%

If every square is one whole, or 100%, each quadrant should be 25%. Both squares combined are 200%, so one 25% shaded quadrant missing would result in 175% of the two squares shaded... hope this helps.

Please help me!!! ASAP!

Answers

Option C

Olivia paid $ 15683.28 after 8 years

evaluate −2xy−1 when y=−1

Answers

Answer:

2x-1

Step-by-step explanation:

Jessica and Monte sell bananas at a produce stand. Jessica earns $4 for each crate of bananas she sells. At the end of the week, Monte has earned $15 less than Jessica. The following expression shows Monte's earnings:

4y − 15

In the expression, what does the first term represent?

Jessica's earnings at the end of the week
The number of crates of bananas Jessica sold
Monte's earnings at the end of the week
The number of crates of bananas Monte sold

Answers

Answer:

Jessica's Earning's at the end of the week

Step-by-step explanation:

If Jessica earns $4 for every crate she sells that means the first term would be what Jessica earned at the end of the week minus $15 because Monte made $15 dollars less then Jessica.

In the expression the first term represents "The number of crates of bananas Monte sold". So option D is correct.

What are expressions?

An expression is a sentence with at least two numbers or variables having mathematical operation. Maths operations can be subtraction, multiplication, addition,  division.

For example, 2x+3

The expression given for Monte's earnings is 4y - 15.

In this expression, the first term is 4y.

This term represents the amount of money Monte earns per crate of bananas he sells.

Therefore, the first term represents the rate of pay for Monte's earnings, which is $4 per crate.

So, the answer is: The first term represents the amount of money Monte earns per crate of bananas he sells.

To know more about Expressions check:

brainly.com/question/16804733

#SPJ3

Find all the two-digit numbers that decrease 12 times when the last digit is crossed out.

Answers

Answer:

Step-by-step explanation:

8 tens + 3 ones = ____ tens + 13 ones

Answers

Answer:

7 tens

Step-by-step explanation:

the value of the first half of the statement is 83 and the value of the second one is 13 (without the tens) so that mean it has 70 left over to make it 7 tens.

A juice box has a length of 2 inches, a width of 1 inch, and a height of 4 inches. What is the volume of the juice box?

Answers

Answer:

8 in

Step-by-step explanation:

L × W × H = V2 × 1 × 4 = 8 in

I hope this helps!

Multiply -2.6 (-3.4)=

Answers

Answer:

8.84

Step-by-step explanation:

Answer:

8.84

Step-by-step explanation:

Help out asap please!

Answers

Answer:1<x_<6 and the third line thing w the open circle (1) connecting to closed circle (6)

Step-by-step explanation:subtract 5 from both sides,

Rachel is recording the temperature at her school every morning this week. On Monday, the temperature was 5°C. Part A: On Wednesday, Rachel calculated that the temperature was 13 degrees colder than Monday. What temperature did Rachel record on Wednesday? Part B: On Friday, Rachel calculated that the temperature was 4 degrees warmer than Wednesday. What temperature did Rachel record on Friday?​

Answers

Answer:

Part A: -8

Part B: -4

Step-by-step explanation:

[tex]5-13=-8[/tex]

[tex]-8+4=-4[/tex]

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