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Please, I want to solve this question
2· Let 0 < p < 0.5. Assume that...
You have 5 coins, four of which are fair coins, i.e. P(H)=P(T)= 0.5, and the other...
You have 5 coins, four of which are fair coins, i.e. P(H)=P(T)= 0.5, and the other of which is a two headed coin, i.e. both sides have a head. Suppose you select a coin at random and flip in 3 times, getting all heads. If you flip the coin again, what is the probability it will be heads?
Suppose C1;C2;C3 are three didifferent biased coins, whose probability of heads equals 0.4, 0.5, and 0.2...
Suppose C1;C2;C3 are three didifferent biased coins, whose probability of heads equals 0.4, 0.5, and 0.2 respectively. Suppose coins are placed together in a box and you randomly picked a coin from the box. Flip the coin 10 times. Let A denote the event you randomly chose coin C1. Let B denote the event that you got exactly 4 heads out of the 10 coin flips. Compute the following probabilities: P(A∩B) P(B) P(A|B)
Mysterioso the Magician is walking down the street with a box containing 25 identical looking coins: 24 are fair coins (which flip heads with probability 0.5 and tails with probability 0.5) and one i...
Mysterioso the Magician is walking down the street with a box containing 25 identical looking coins: 24 are fair coins (which flip heads with probability 0.5 and tails with probability 0.5) and one is a trick coin which alwavs flips heads. Renata the Fox skillfully robs Mysterioso of one of the coins in his box (chosen uniformly at random). She decides she will flip the coin k times to test if it is the trick coin. (a) What is the...
2. Mysterioso the Magician is walking down the street with a box containing 25 identical looking coins: 24 are fair coins (which flip heads with probabilty 0.5 and tails with probability 0.5) and one...
2. Mysterioso the Magician is walking down the street with a box containing 25 identical looking coins: 24 are fair coins (which flip heads with probabilty 0.5 and tails with probability 0.5) and one is a trick coin which always flips heads. Renata the Fox skillfully robs Mysterioso of one of the coins in his box (chosen uniformly at random). She decides she will flip the coin k times to test if it is the trick coin (a) What is...
Coin with random bias. Let P be a random variable distributed uniformly over [0, 1]. A...
Coin with random bias. Let P be a random variable distributed uniformly over [0, 1]. A coin with (random) bias P (i.e., Pr[H] = P) is flipped three times. Assume that the value of P does not change during the sequence of tosses. a. What is the probability that all three flips are heads? b. Find the probability that the second flip is heads given that the first flip is heads. c. Is the second flip independent of the first...
Q 2. There are two coins, one fair and one biased with P[H] = 0:4. A...
Q 2. There are two coins, one fair and one biased with P[H] = 0:4. A game is played by successively flipping the coins as follows: The game begins with a flip of the fair coin, and the result, H or T, is noted. If the result of the flip is H, then the other coin is used on the next flip, and the result is noted. If the result of a flip is T, then the same coin is...
A biased coin is tossed n times. The probability of heads is p and the probability of tails is q and p=2q. Choose all correct statements. This is an example of a Bernoulli trial n-n-1-1-(k-1) p...
A biased coin is tossed n times. The probability of heads is p and the probability of tails is q and p=2q. Choose all correct statements. This is an example of a Bernoulli trial n-n-1-1-(k-1) p'q =np(p + q)n-1 = np f n- 150, then EX), the expected value of X, is 100 where X is the number of heads in n coin tosses. f the function X is defined to be the number of heads in n coin tosses,...
Q.1 (25') Pony is playing coin tossing game with Yanny. They found the coin have 4...
Q.1 (25') Pony is playing coin tossing game with Yanny. They found the coin have 4 heads and 6 tails in 10 flips. Let p be the probability for obtaining a head, based on the first 10 flips a) Can we conclude it is a biased or fair coin base on the result above? b) Plot the Bernoulli's PMF What is the probability for obtaining 6 heads in 10 flips using the same coin? d) What is the probability for...
Suppose there are two coins. One is a standard fair coin, so that P(heads)=0.50. The other...
Suppose there are two coins. One is a standard fair coin, so that P(heads)=0.50. The other one is a two-sided coin, so that P(heads)=1. You draw one of the two coins at random and toss it. It results in heads. Given that observation... (a) Compute the probability that you have selected a fair coin. (1pt) (b) What is the probability that the next toss will result in heads too? (1pt) (c) If the next toss results in heads as well,...
1. A jar has two kinds of coins. Some of them are fair, and some of them have are biased, in whic...
1. A jar has two kinds of coins. Some of them are fair, and some of them have are biased, in which case P(heads) = 2 . 3 A coin is selected from the jar. Since we don’t know which kind it is, we toss it 50 times. Let X be the number of heads that occur. Please note carefully the directions of the inequalities (≤ or ≥) in each of the questions below. (a) Suppose the coin chosen is...
Mysterioso the Magician is walking down the street with a box containing 25 identical looking coins: 24 are fair coins (which flip heads with probability 0.5 and tails with probability 0.5) and one is a trick coin which alwavs flips heads. Renata the Fox skillfully robs Mysterioso of one of the coins in his box (chosen uniformly at random). She decides she will flip the coin k times to test if it is the trick coin. (a) What is the...
2. Mysterioso the Magician is walking down the street with a box containing 25 identical looking coins: 24 are fair coins (which flip heads with probabilty 0.5 and tails with probability 0.5) and one is a trick coin which always flips heads. Renata the Fox skillfully robs Mysterioso of one of the coins in his box (chosen uniformly at random). She decides she will flip the coin k times to test if it is the trick coin (a) What is...
Coin with random bias. Let P be a random variable distributed uniformly over [0, 1]. A coin with (random) bias P (i.e., Pr[H] = P) is flipped three times. Assume that the value of P does not change during the sequence of tosses. a. What is the probability that all three flips are heads? b. Find the probability that the second flip is heads given that the first flip is heads. c. Is the second flip independent of the first...
A biased coin is tossed n times. The probability of heads is p and the probability of tails is q and p=2q. Choose all correct statements. This is an example of a Bernoulli trial n-n-1-1-(k-1) p'q =np(p + q)n-1 = np f n- 150, then EX), the expected value of X, is 100 where X is the number of heads in n coin tosses. f the function X is defined to be the number of heads in n coin tosses,...
Q.1 (25') Pony is playing coin tossing game with Yanny. They found the coin have 4 heads and 6 tails in 10 flips. Let p be the probability for obtaining a head, based on the first 10 flips a) Can we conclude it is a biased or fair coin base on the result above? b) Plot the Bernoulli's PMF What is the probability for obtaining 6 heads in 10 flips using the same coin? d) What is the probability for...
Suppose there are two coins. One is a standard fair coin, so that P(heads)=0.50. The other one is a two-sided coin, so that P(heads)=1. You draw one of the two coins at random and toss it. It results in heads. Given that observation... (a) Compute the probability that you have selected a fair coin. (1pt) (b) What is the probability that the next toss will result in heads too? (1pt) (c) If the next toss results in heads as well,...
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