Question

In: Statistics and Probability

Your unfair coin comes up heads with probability 0.6. You flip it until you get four...

Your unfair coin comes up heads with probability 0.6. You flip it until you get four heads in a row. Let t be the expected number of times you flip. Write an equation for t. (Your equation, if solved, should give the value of t).

Solutions

Expert Solution


Related Solutions

Coin 1 comes up heads with probability 0.6 and coin 2 with probability 0.5. A coin...
Coin 1 comes up heads with probability 0.6 and coin 2 with probability 0.5. A coin is continually flipped until it comes up tails, at which time that coin is put aside and we start flipping the other one. (a) What proportion of flips use coin 1? (b) If we start the process with coin 1 what is the probability that coin 2 is used on the fifth flip? (c) What proportion of flips land heads?
) Suppose you flip a coin. If it comes up heads, you win $20; if it...
) Suppose you flip a coin. If it comes up heads, you win $20; if it comes up tails, you lose $20. a) Compute the expected value and variance of this lottery. b) Now consider a modification of this lottery: You flip two fair coins. If both coins come up heads, you win $20. If one coin comes up heads and the other comes up tails, you neither win nor lose – your payoff is $0. If both coins come...
Suppose you flip a biased coin (that lands heads with probability p) until 2 heads appear....
Suppose you flip a biased coin (that lands heads with probability p) until 2 heads appear. Let X be the number of flips needed for this two happen. Let Y be the number of flips needed for the first head to appear. Find a general expression for the condition probability mass function pY |X(i|n) when n ≥ 2. Interpret your answer, i.e., if the number of flips required for 2 heads to appear is n, what can you say about...
1. A) If you flip an unfair coin 100 times, and the probability for a coin...
1. A) If you flip an unfair coin 100 times, and the probability for a coin to be heads is 0.4, then the number of heads you expect on average is: B) If you flip an unfair coin 100 times, and the probability for a coin to be heads is 0.4, then the standard deviation for the number of heads is: C) If you flip an unfair coin 2 times, and the probability for a coin to be heads is...
Flip a coin 10 times. Put a 1 each time the coin comes up heads and...
Flip a coin 10 times. Put a 1 each time the coin comes up heads and a 0 each time the coin comes up tails. Count the number of heads you obtained and divide by 10. What number did you get? a. Is the number you obtained in part (a) a parameter or a statistic? b. Now flip the coin 25 times. Put a 1 each time you obtain a heads and a 0 for tails. Count the number of...
If you flip a fair coin, the probability that the result is heads will be 0.50....
If you flip a fair coin, the probability that the result is heads will be 0.50. A given coin is tested for fairness using a hypothesis test of H0:p=0.50 versus HA:p≠0.50. The given coin is flipped 180 times, and comes up heads 110 times. Assume this can be treated as a Simple Random Sample. The test statistic for this sample z and the p value
30.Consider a coin that comes up heads with probability p and tails with probability 1 −...
30.Consider a coin that comes up heads with probability p and tails with probability 1 − p. Let qn be the probability that after n independent tosses, there have been an even number of heads. Derive a recursion that relates qn to qn−1, and solve this recursion to establish the formula qn = 1 + (1 − 2p) n 2 Using method other than Mathematical Induction
In a sequence of independent flips of a fair coin thwr comes up heads with probability...
In a sequence of independent flips of a fair coin thwr comes up heads with probability 0.6, what is the probability that there is a run of three consecutive heads within the first 10 flips? Show a Markov chain that counts the number of consecutive heads attained.
You are given an unfair coin (the probability of heads is 1/3) and decide to toss...
You are given an unfair coin (the probability of heads is 1/3) and decide to toss it ten times. Following Example 5.3 in your textbook, plot the binomial probability mas function for N = 10 and p = 1/3. What is the probability that the coin will come up heads 5 times in 10 tosses? Determine the mean, variance, and joint second moments. a. Y = cos
Suppose that we flip a fair coin until either it comes up tails twice or we...
Suppose that we flip a fair coin until either it comes up tails twice or we have flipped it six times. What is the expected number of times we flip the coin?
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT