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?

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).

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

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​

8 tens + 3 ones = ____ tens + 13 ones

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

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.

Please help answer this for me :)

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

each square below represents one whole​

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

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

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.

HELP ASAP PLEASE!!!!!!!!

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?

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

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

evaluate −2xy−1 when y=−1

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.​

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?

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

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?​

Help out asap please!

Multiply -2.6 (-3.4)=

Please help me!!! ASAP!

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

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?

Simplify the given expressions.

(7−2)2−(2+1)(2−5)

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)

What’s the slope of (-8,2) (1,9)

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

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?