Question

In: Math

A machine produces coins such that the probability of heads, p, follows a Beta distribution with...

A machine produces coins such that the probability of heads, p, follows a Beta distribution with parameters (α, β) = (1, 1). A coin produced by this machine is picked at random and tossed independently n times. Let Y be the number of heads.

  1. (a) Find E[Y ].

  2. (b) Write down the pmf for Y (your answer can include unevaluated integrals and

    combination numbers [aka “n choose m” symbols]).

Solutions

Expert Solution

the expectation of binomial distribution,

milcah answered 1 hour ago
< Previous

Related Solutions

Problem 4) Five coins are flipped. The first four coins will land on heads with probability...
Problem 4) Five coins are flipped. The first four coins will land on heads with probability 1/4. The fifth coin is a fair coin. Assume that the results of the flips are independent. Let X be the total number of heads that result. (hint: Condition on the last flip). a) Find P(X=2) b) Determine E[X]
A box contains 5 fair coins, 4 coins that land heads with probability 1/3 , and...
A box contains 5 fair coins, 4 coins that land heads with probability 1/3 , and 1 coin that lands heads with probability 1/4 . A coin is taken from the box at random and flipped repeatedly until it has landed heads three times. Let X be the number of times that the coin is flipped and Y be the probability that the coin lands heads. (a) Find the random variables E(X|Y ) and var(X|Y ) in terms of Y...
A box contains 5 fair coins, 4 coins that land heads with probability 1/3 , and...
A box contains 5 fair coins, 4 coins that land heads with probability 1/3 , and 1 coin that lands heads with probability 1/4 . A coin is taken from the box at random and flipped repeatedly until it has landed heads three times. Let X be the number of times that the coin is flipped and Y be the probability that the coin lands heads. (a) Find the random variables E(X|Y ) and var(X|Y ) in terms of Y...
A box contains 5 fair coins, 4 coins that land heads with probability 1/3 , and...
A box contains 5 fair coins, 4 coins that land heads with probability 1/3 , and 1 coin that lands heads with probability 1/4 . A coin is taken from the box at random and flipped repeatedly until it has landed heads three times. Let X be the number of times that the coin is flipped and Y be the probability that the coin lands heads. (a) Find the random variables E(X|Y ) and var(X|Y ) in terms of Y...
For the following exercises, four coins are tossed. Find the probability of tossing either two heads or three heads.
For the following exercises, four coins are tossed.Find the probability of tossing either two heads or three heads.
In tossing three fair coins, what is the probability of getting at least two heads?
In tossing three fair coins, what is the probability of getting at least two heads?
You have 100 coins, and 99 of them are fair (equal probability of heads or tails)....
You have 100 coins, and 99 of them are fair (equal probability of heads or tails). One of them is weighted and has a 90% probability of landing on heads. You randomly choose one of the 100 coins. Find the probability that it is a weighted coin, under the following scenarios: (Hint: if your calculator can’t compute 100!, R can, just type factorial(100)) (a) You flip it 10 times and lands on heads 10 times (b) You flip it 10...
1st Case: What is the probability of getting 3 heads when 10 coins are tossed? 2nd...
1st Case: What is the probability of getting 3 heads when 10 coins are tossed? 2nd Case:What is the probability of getting 3 or less heads when 10 coins are tossed? 3rd Case: What is the probability of getting 3 or less heads when 10 coins are tossed? Don't use Excel
Three fair coins are tossed simultaneously 10 times. Find the probability that "2 heads and one...
Three fair coins are tossed simultaneously 10 times. Find the probability that "2 heads and one tail" will show up (a) at least once and (b) at most once.
Begin by creating a probability distribution for the number of heads in five tosses of a...
Begin by creating a probability distribution for the number of heads in five tosses of a coin. List the different possible outcomes. Calculate the expected value of the random variable. Calculate the standard deviation of this distribution.
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT