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Exercise 5 (a) Suppose a fair coin is tossed n times. The reward in obtaining X...
A fair coin is tossed n times. Each coin toss costs d dollars and the reward...
A fair coin is tossed n times. Each coin toss costs d dollars and the reward in obtaining X heads is aX2 +bX. Find the expected value of the net reward.
QUESTION 8 Problem 8) A fair coin is tossed 20 times. A fair coin means that...
QUESTION 8 Problem 8) A fair coin is tossed 20 times. A fair coin means that the probability of getting a head is the same as the probability of getting a tail. Let X be the number of coins of getting head. Note that there are only two possible outcomes: getting head or tail after tossing the coin. X follows a binomial distribution with n=20, p=0.5. Answer the following questions. (Question) Find the expected value of X, E(X). QUESTION 9...
A fair coin is tossed eight times. Calculate (e) the probability of obtaining exaectly 4 heads...
A fair coin is tossed eight times. Calculate (e) the probability of obtaining exaectly 4 heads (b) the probability of obtaining exactly 3 heads (c) the probability of obtaining 3, 4 or 5 heads.
5. (15 pts) a) A coin is tossed 5 times. Let X be the number of...
5. (15 pts) a) A coin is tossed 5 times. Let X be the number of Heads on the first 4 tosses and Y be the number of Heads on the last three tossed. Find the joint probabilities Pij = P(X = 1, Y = j) for all relevant i and j. Find the marginal probabilities pit and p+, for all relevant i and j. b) Find the value of A that would make the function Af(x,y) a PDF. Where...
Suppose a fair coin is tossed 280 times. Find the probability that the number of Heads...
Suppose a fair coin is tossed 280 times. Find the probability that the number of Heads observed is 151 or more. Use Binomial Distribution and Normal Approximation and compare the results.
Suppose that a coin with probability 0.7 of heads is tossed 100 times. Let X be...
Suppose that a coin with probability 0.7 of heads is tossed 100 times. Let X be the number of heads obtained. What is the probability of obtaining a streak of at least 15 consecutive heads in the 100 tosses?
Suppose that a coin is tossed three times. We assume that a coin is fair, so...
Suppose that a coin is tossed three times. We assume that a coin is fair, so that the heads and tails are equally likely. Probability that two heads are obtained in three tosses given that at least one head is obtained in three tosses is ___________ Probability that that one head is obtained in three tosses given that at most one head is obtained in three tosses is ____________ at least one means one or more, at most one means...
A fair coin is tossed 3 times. Let X denote a 0 if the first toss...
A fair coin is tossed 3 times. Let X denote a 0 if the first toss is a head or 1 if the first toss is a zero. Y denotes the number of heads. Find the distribution of X. Of Y. And find the joint distribution of X and Y.
A fair coin is tossed three times. Let X be the number of heads that come...
A fair coin is tossed three times. Let X be the number of heads that come up. Find the probability distribution of X X 0 1 2 3 P(X) 1/8 3/8 3/8 1/8 Find the probability of at least one head Find the standard deviation σx
Problem 10) A fair coin is tossed 20 times. A fair coin means that the probability...
Problem 10) A fair coin is tossed 20 times. A fair coin means that the probability of getting a head is the same as the probability of getting a tril. Let X be the number of coins of getting head. Note that there are only two possible outcomes: getting head or tail after tossing the coin X follows a binomial distribution with n =20, p=0.5. Answer the following questions (Question) Find PX-17).
A fair coin is tossed n times. Each coin toss costs d dollars and the reward in obtaining X heads is aX2 +bX. Find the expected value of the net reward.
QUESTION 8 Problem 8) A fair coin is tossed 20 times. A fair coin means that the probability of getting a head is the same as the probability of getting a tail. Let X be the number of coins of getting head. Note that there are only two possible outcomes: getting head or tail after tossing the coin. X follows a binomial distribution with n=20, p=0.5. Answer the following questions. (Question) Find the expected value of X, E(X). QUESTION 9...
A fair coin is tossed eight times. Calculate (e) the probability of obtaining exaectly 4 heads (b) the probability of obtaining exactly 3 heads (c) the probability of obtaining 3, 4 or 5 heads.
5. (15 pts) a) A coin is tossed 5 times. Let X be the number of Heads on the first 4 tosses and Y be the number of Heads on the last three tossed. Find the joint probabilities Pij = P(X = 1, Y = j) for all relevant i and j. Find the marginal probabilities pit and p+, for all relevant i and j. b) Find the value of A that would make the function Af(x,y) a PDF. Where...
Problem 10) A fair coin is tossed 20 times. A fair coin means that the probability of getting a head is the same as the probability of getting a tril. Let X be the number of coins of getting head. Note that there are only two possible outcomes: getting head or tail after tossing the coin X follows a binomial distribution with n =20, p=0.5. Answer the following questions (Question) Find PX-17).
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