Question

In: Statistics and Probability

A player tosses a fair coin n times. Each time, if the coin lands on Head,...

A player tosses a fair coin n times. Each time, if the coin lands on Head, the player win a dollar, otherwise, the player loses a dollar. What is the expected earning of the player? What is the variance of the earning of the player? Now the player apply a new strategy: the player will play the game until he gets a head. What is the expected earning of the new strategy? Does the result depend on n?

Solutions

Expert Solution

orchestra answered 2 years ago
Next > < Previous

Related Solutions

A fair coin will be tossed three times. (a) Indicating a head by H and a...
A fair coin will be tossed three times. (a) Indicating a head by H and a tail by T write down the outcome space. (b) What is the probability that on the first toss the outcome with a tail? (c) What is the probability of obtaining exactly two heads from the three coin tosses? (d) What is the probability that the first toss gives a tail and exactly two heads are obtained from the three coin tosses? Are the outcomes...
Fair Coin? A coin is called fair if it lands on heads 50% of all possible...
Fair Coin? A coin is called fair if it lands on heads 50% of all possible tosses. You flip a game token 100 times and it comes up heads 41 times. You suspect this token may not be fair. (a) What is the point estimate for the proportion of heads in all flips of this token? Round your answer to 2 decimal places. (b) What is the critical value of z (denoted zα/2) for a 99% confidence interval? Use the...
A coin that lands on heads with a probability of p is tossed multiple times. Each...
A coin that lands on heads with a probability of p is tossed multiple times. Each toss is independent. X is the number of heads in the first m tosses and Y is the number of heads in the first n tosses. m and n are fixed integers where 0 < m < n. Find the joint distribution of X and Y.
Madi and Alex are both tossing a fair coin. Madi tosses hers 10 times and Alex...
Madi and Alex are both tossing a fair coin. Madi tosses hers 10 times and Alex tosses his 30 times. Which of them is more likely to get more than 60% heads or do they have the same chance? Explain why? 1.) Describe a model for Madi and Alex's coin tossing. What measures can help you decide who is more likely to get more than 60% or if they are equally likely. 2.) If you gave students this problem without...
sean tosses a coin 40 times and gets 15 heads while Micah tosses a coin 30...
sean tosses a coin 40 times and gets 15 heads while Micah tosses a coin 30 times and gets 16 heads. Suppose that the outcomes of sean's coin tosses are iid random variable with probability p1 of getting heads on each toss while Micah’s outcomes are also iid with a potentially different probability p2 of getting heads. (1) Calculate the maximum likelihood and method of moments estimators of p1. (2) Show that the MLE of p1 is an MVUE for...
8. A fair coin is tossed 60 times. Find the probability that the head appears between...
8. A fair coin is tossed 60 times. Find the probability that the head appears between 22 and 40 times by using a. binomial distribution, b. approximation of Binomial distribution by normal distribution. Discuss why b. is better in practice.
hink about the following game: A fair coin is tossed 10 times. Each time the toss...
hink about the following game: A fair coin is tossed 10 times. Each time the toss results in heads, you receive $10; for tails, you get nothing. What is the maximum amount you would pay to play the game? Define a success as a toss that lands on heads. Then the probability of a success is 0.5, and the expected number of successes after 10 tosses is 10(0.5) = 5. Since each success pays $10, the total amount you would...
Consider an experiment: tossing a coin three times, and observe head/tail facing up for each time....
Consider an experiment: tossing a coin three times, and observe head/tail facing up for each time. a) What is the sample space? b) List sample points in the event A that there are more tails than heads. c) List sample points in the event B that exact 2 tails face up. d) find the probabilities: P[A], P[B], P[A∩ B], P[AU B].
Fair Coin? In a series of 100 tosses of a token, the proportion of heads was...
Fair Coin? In a series of 100 tosses of a token, the proportion of heads was found to be 0.43. However, the margin of error for the estimate on the proportion of heads in all tosses was too big. Suppose you want an estimate that is in error by no more than 0.05 at the 90% confidence level. (a) What is the minimum number of tosses required to obtain this type of accuracy? Use the prior sample proportion in your...
Fair Coin? In a series of 100 tosses of a token, the proportion of heads was...
Fair Coin? In a series of 100 tosses of a token, the proportion of heads was found to be 0.43. However, the margin of error for the estimate on the proportion of heads in all tosses was too big. Suppose you want an estimate that is in error by no more than 0.03 at the 95% confidence level. (a) What is the minimum number of tosses required to obtain this type of accuracy? Use the prior sample proportion in your...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT