Flip a fair coin n times. Let
2. We flip a fair coin 5 times. Let A be the event that at least one T was flipped immediately after an H (i.e. the combination HT appears at least once in your sequence of flips). Use a Markov chain to compute P(A). Hint: Try using the following three states for your Markov chain: State 0: HT has not appeared yet and cannot appear in the next flip; State 1: HT has not appeared yet, but could appear in...
We flip a fair coin 5 times. Let A be the event that at least one T was flipped immediately after an H (i.e. the combination HT appears at least once in your sequence of flips). Use a Markov chain to compute P(A). Hint: Try using the following three states for your Markov chain: State 0: HT has not appeared yet and cannot appear in the next flip; State 1: HT has not appeared yet, but could appear in the...
Exercise 1.16. We flip a fair coin five times. For every heads you pay me $1 and for every tails I pay you $1. Let X denote my net winnings at the end of five flips. Find the possible values and the probability mass function of X.
Suppose we flip a fair coin n times. We say that the sequence is balanced when there are equal number of heads and tails. For example, if we flip the coin 10 times and the results are HT HHT HT T HH, then this sequence balanced 2 times, i.e. at position 2 and position 8 (after the second and eighth flips). In terms of n, what is the expected number of times the sequence is balanced within n flips?
Suppose that I flip a fair coin 21 times. What is the probability that it will land on heads exactly 13 times?
Suppose that I flip a fair coin 36 times. What is the probability that it will land on heads exactly 23 times?
A fair coin is flipped until the first head appears. Let X= the total number of times the coin is flipped. Find E(x). Hint:if the first flip is tails, this "game" restarts.
Suppose that I flip a fair coin 21 times. What is the probability that it will land on heads exactly 12 times? Round to 4 decimal places.
We flip a fair coin 10 times. What is the probability that there are at least 4 heads out of the 10 flips?
Coin Flips: If you flip a fair coin 5 times, what is the probability of each of the following? (please round all answers to 4 decimal places) a) getting all tails? b) getting all heads?