Suppose you toss an unfair coin 8 times independently. The probability ofgetting a head is 0.3....
Suppose you toss an unfair coin 8 times independently. The probability ofgetting a head is 0.3. Denote the outcome to be 1 if you get a head and 0 if a tail.
(i) Write down the sample space Ω.
(ii) What is the probability of the event that you get a head or a tail at least once?
(iii) If you get eight same toss's you will get x dollars, otherwise you will lose 1 dollar. On average, how large should x be to guarantee that you will not lose money in the long run?
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Suppose you toss an unfair coin 8 times independently. The
probability ofgetting a head is 0.3....
5. You play a game using an unfair coin. Suppose that each time the coin is...
5. You play a game using an unfair coin. Suppose that each time the coin is tossed, the probability of showing "head" is 1/3 and the probability of showing "tail" is 2/3. Also suppose that each time the coin shows head you win 10 dollars and you lose 3 dollars when it shows tail. How much money do you expect to win when the coin is tossed 10 times?
An unfair coin is flipped. If a head turns up, you win $1. If a tail...
An unfair coin is flipped. If a head turns up, you win $1. If a tail turns up, you lose $1. The probability of a head is.36 and the probability of a tail is .64. Let X be the random variable for the amount won on a single play of this game. What is the expected value of the game? E(X)= dollars (Type an integer or a decimal. Round to the nearest cent as needed.)
Suppose you are playing two unfair coins. The probability of tossing a tail is θ for...
Suppose you are playing two unfair coins. The probability of
tossing a tail is θ for coin 1, and 2θ for coin 2. You toss each
coin several times, and you get the following results:
(a) What is the probability of tossing a head for coin 1 and for
coin 2 [3pts]?
(b) What is the likelihood of the data given θ [7pts]?
(c) What is maximum likelihood estimation for θ [7pts]?
Coin No.Result head head tail head tail tail
An unfair coin is flipped. If a head turns up, you win $1. If a tail...
An unfair coin is flipped. If a head turns up, you win $1. If a tail turns up, you lose $1. The probability of a head is .61 and the probability of a tail is .39 Let X be the random variable for the amount won on a single play of this game. What is the expected value of the game?
Suppose you are playing two unfair coins. The probability of tossing a tail is θ for...
Suppose you are playing two unfair coins. The probability of tossing a tail is θ for coin 1, and 2θ for coin 2. You toss each coin for several times, and you get the following results: (a) What is the probability of tossing a head for coin 1 and for coin 2? coin no. result 1 head 2 head 1 tail 1 head 2 tail 2 tail (b) What is the likelihood of the data given ? (c) What is...
Problem(13) (10 points) An unfair coin is tossed, and it is assumed that the chance of...
Problem(13) (10 points) An unfair coin is tossed, and it is assumed that the chance of getting a head, H. is (Thus the chance of setting tail, T. is.) Consider a random experiment of throwing the coin 5 times. Let S denote the sample space (a) (2 point) Describe the elements in S. (b) (2 point) Let X be the random variable that corresponds to the number of the heads coming up in the four times of tons. What are...
9.74. Suppose we toss a biased coin independently until we get two heads or two tails...
9.74. Suppose we toss a biased coin independently until we get two heads or two tails in total. The coin produces a head with probability p on any toss. 1. What is the sample space of this experiment? 2. What is the probability function? 3. What is the probability that the experiment stops with two heads?
Imagine an experiment where we flip a coin 6 times, and get “head, tail, head, head,...
Imagine an experiment where we flip a coin 6 times, and get “head, tail, head, head, head, head”. Which of the following statements are true? a) The coin is not fair b) The coin’s tail probability is 1/6 c) The sequence "head, tail, head, head, head, head" is an outcome in the sample space. d) The sample space of the experiment is {head, tail}
2 Maximum Likelihood [25pts] 2.1 Discrete Example 17pts) Suppose you are playing two unfair coins. The...
2 Maximum Likelihood [25pts] 2.1 Discrete Example 17pts) Suppose you are playing two unfair coins. The probability of tossing a tail is θ for coin 1, and 20 for coin 2. You toss each coin for several times, and you get the following results: (a) What is the probability of tossing a head for coin 1 and for coin 2 3pts? Coin No. eult head head tail head tail tail (b) what is the likelihood of the data given θ...
Suppose we toss a weighted coin, for which the probability of getting a head (H) is...
Suppose we toss a weighted coin, for which the probability of getting a head (H) is 60% i) If we toss this coin 3 times, then the probability of getting exactly two heads (to two decimal places) is Number ii) If we toss this coin 6 times, then the probability of getting exactly four heads (to two decimal places) is Number CI iii) if we toss this coin 8 times, then the probability of getting 6 or more heads (to...
5. You play a game using an unfair coin. Suppose that each time the coin is tossed, the probability of showing "head" is 1/3 and the probability of showing "tail" is 2/3. Also suppose that each time the coin shows head you win 10 dollars and you lose 3 dollars when it shows tail. How much money do you expect to win when the coin is tossed 10 times?
An unfair coin is flipped. If a head turns up, you win $1. If a tail turns up, you lose $1. The probability of a head is.36 and the probability of a tail is .64. Let X be the random variable for the amount won on a single play of this game. What is the expected value of the game? E(X)= dollars (Type an integer or a decimal. Round to the nearest cent as needed.)
Suppose you are playing two unfair coins. The probability of
tossing a tail is θ for coin 1, and 2θ for coin 2. You toss each
coin several times, and you get the following results:
(a) What is the probability of tossing a head for coin 1 and for
coin 2 [3pts]?
(b) What is the likelihood of the data given θ [7pts]?
(c) What is maximum likelihood estimation for θ [7pts]?
Coin No.Result head head tail head tail tail
Problem(13) (10 points) An unfair coin is tossed, and it is assumed that the chance of getting a head, H. is (Thus the chance of setting tail, T. is.) Consider a random experiment of throwing the coin 5 times. Let S denote the sample space (a) (2 point) Describe the elements in S. (b) (2 point) Let X be the random variable that corresponds to the number of the heads coming up in the four times of tons. What are...
2 Maximum Likelihood [25pts] 2.1 Discrete Example 17pts) Suppose you are playing two unfair coins. The probability of tossing a tail is θ for coin 1, and 20 for coin 2. You toss each coin for several times, and you get the following results: (a) What is the probability of tossing a head for coin 1 and for coin 2 3pts? Coin No. eult head head tail head tail tail (b) what is the likelihood of the data given θ...
Suppose we toss a weighted coin, for which the probability of getting a head (H) is 60% i) If we toss this coin 3 times, then the probability of getting exactly two heads (to two decimal places) is Number ii) If we toss this coin 6 times, then the probability of getting exactly four heads (to two decimal places) is Number CI iii) if we toss this coin 8 times, then the probability of getting 6 or more heads (to...
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