# probablity

We are given a biased coin , where the probability of heads is q. he bias q is itself the realization of a random variable Q which is uniformly distributed on the interval [0,1]. We want to estimate the bias of the coin. We flip it 5 times, and define the(observed) random variable N as the number of heads in the experiment. Throughout this problem, you may find the following formula useful: x^n(1-x)^kdx= n!k!/(n+k+1)!.
1.Given the observation N=3. Calculate the posterior distribution of the bias Q.
2.What is the LMS estimate of Q, given N=3.
3.What is the resulting conditional mean squared error of the LMS estimator, given N=3.

1. 👍 0
2. 👎 0
3. 👁 361

## Similar Questions

Please check my work thanks!! A number cube with the numbers 1 through 6 is rolled. Find the given probability. 1. P(number < 2) (1 point) A. 1/6

asked by Matthew on March 6, 2013
2. ### Math

Alice has two coins. The probability of Heads for the first coin is 1/4, and the probability of Heads for the second is 3/4. Other than this difference, the coins are indistinguishable. Alice chooses one of the coins at random and

asked by Anonymous on July 23, 2019
3. ### english

1. Which of the following sources is least likely to have been edited for accuracy? (1 point) a city newspaper a personal Web site an encyclopedia article a published book 2. Which of the following is NOT true about bias? (1

asked by kate on August 15, 2014
4. ### Math

A coin is biased so that a head is twice as likely to occur as a tail. If the coin is tossed 3 times, what is the probability of getting 2 tails and 1 head? What do you mean by biased in probability?

asked by Jen on October 15, 2015
5. ### CALC

A biased coin whose chance of heads is 0.4 is tossed five times in a row. What is the probability that heads is tossed exactly 2 times? 20.2% 23.04% 36.8% 40.1% 45.6%

asked by Leandra on November 27, 2012
1. ### Probability

We have a red coin, for which P(Heads)=0.4, a green coin, for which P(Heads)=0.5 and a yellow coin for which P(Heads)=0.6. The flips of the same or of different coins are independent. For each of the following situations,

asked by Alex on November 24, 2018
2. ### math

We are given a biased coin, where the (random) bias Θ is uniformly distributed on [0,1] . We toss this coin, until we see Heads for the first time. Our goal is to estimate Θ using our observation. Find the LMS estimator ΘˆLMS

asked by x on September 3, 2019
3. ### Stat.

A trick coin has been weighted so that heads occurs with a probability of p  2 3, and p(tails)  1 3. If you toss this coin 72 times, a. How many heads would you expect to get on average? b. What is the probability of getting

asked by Nickie on January 27, 2013
4. ### Probabilty

Biased coin has a 0.4 probability of landing on tails. The random variable x, based on a single toss of the coin, is defined as follows: x=0 if heads appears; x=1 if tails appears. What Is the mean value of X? Is it . 0.3 .4 .6 .5

asked by Gilbert on November 28, 2012
5. ### statistics

A coin is tossed 3 times. Find the probability that all the 3 are heads (A) if it is known that the first is heads (B) if it is known that the first 2 are heads (C) if it is known that the 2 of them are heads

asked by Joseph on February 7, 2015
6. ### probability

A coin is biased such that a head is thrice as likely to occur as a tail. Find the probability distribution of heads and also find the mean and variance of the distribution when it is tossed 4 times. See

asked by mohsin on January 21, 2007