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
Katen [24]
3 years ago
15

You have a coin with unknown probability p of coming up heads. You wish to generate a random variable which takes the values 0 a

nd 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?
Mathematics
1 answer:
elixir [45]3 years ago
7 0

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).

You might be interested in
Find the next term in the sequence 1, 4, 9, 16, 25, ….
Agata [3.3K]
The next is 36!!!!  If you notice each time,  you are adding by two more than what you were adding before.  Like,  1+3=4  4+5=9 9+7=16  See?

So,  25+11=36
7 0
3 years ago
Help<br> What is an equation of the line that passes through the points (-4, 4) and (8.1)?
Svetach [21]

Answer:

y = -1/4x +3

Step-by-step explanation:

Hope this helps!

3 0
3 years ago
Write the slope intercept form of the equation.
Elza [17]

Hello!

The slope intercept form equation is shown below.

y=mx+b

In this equation, m represents the slope and b is the y-intercept.

We can just plug in our numbers to find our answer.

y=3x-2

I hope this helps!

4 0
3 years ago
What is the greatest common factor of 3x4, 15x3, 21x2
Sonja [21]

Answer:

3x^2

Step-by-step explanation:

6 0
2 years ago
Please help me
Shtirlitz [24]

I Am Going Ask My teacher. I just screenshot it.

5 0
2 years ago
Other questions:
  • When simplified, what is the value of square root of negative 45 end square root,if i2 = −1?
    10·1 answer
  • Help me asap i will give brainliest
    5·1 answer
  • What divides an angle into two congruent angles?
    12·2 answers
  • Which of the following assets are eligible for 179 expensing?
    6·1 answer
  • If there are 3.28 feet in 1 meter, how many yards are in 8 meters? Round answer to the nearest tenth. (Hint: This problem requir
    7·1 answer
  • I randomly choose a pair of socks per day. I have 12 white socks and 18 black socks. What is the probability that I will have mi
    9·2 answers
  • Which of the following ratios is NOT equivalent to start fraction 4 over 8 end fraction ?
    7·1 answer
  • 17х+3 – 5у + 19 + 10z
    9·1 answer
  • Helpp plsss I neeed to finish this test ASAP plssssssss thank youu helpp me with this question
    9·1 answer
  • How do I write a phrase in words as an algebraic expression for 8/d?
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!