One gambler flips a fair coin in three separate times. Letting a random variable X represent...
One gambler flips a fair coin in three separate times. Letting a random variable X represent his winnings in the following way: He loses $1 if he gets no heads in three flips; he wins $1, $2, and $3 if he obtains 1, 2, or 3 heads, respectively.
(a) Find the probability mass function of X.
(b) Find the probability density function of X.
(c) Find the cumulative distribution function of X.
(d) Find the probability that he wins more than $2.
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One gambler flips a fair coin in three separate times. Letting a
random variable X represent...
Exercise 1.16. We flip a fair coin five times
Exercise 1.16. We flip a fair coin five times. For every heads you pay me $1 and for every tails I pay you $1. Let X denote my net winnings at the end of five flips. Find the possible values and the probability mass function of X.
3. Consider a coin-die experiment: One flips a fair coin at first. If he gets a...
3. Consider a coin-die experiment: One flips a fair coin at first. If he gets a head, then he will roll a 6-sided fair die; otherwise, he will roll a 6-sided unfair die, which has probability to get i faces up (i = i, . . . , 6). If one gets a 2 faces up, what is the probability that he got a tail when he flipped the coin? 2.1
Let X equal to the number of heads after 4 flips of a fair coin? Derive...
Let X equal to the number of heads after 4 flips of a fair coin? Derive the probability mass function for X, and plot it. Also, compute the E[X] of X.
(10 pts) In a game, a player flips a coin three times. The player wins $3...
(10 pts) In a game, a player flips a coin three times. The player wins $3 for every head that turns up. The player must pay S5 to play the game. Let the random variable W represent the total winnings after playing the game. (a) Construct the pmf of W (b) Find the expectation and variance of W. (c) Would you play the game? Why or why not?
Tom has three coins. Two are fair and one is unfair coin weighted so that heads...
Tom has three coins. Two are fair and one is unfair coin weighted so that heads is three times as likely as tails. He selects one of the coins at random and flips it. What is the probability it comes up heads? If it does come up heads, what is the probability it was the unfair coin?
Question 3 (15 pts). A gambler plays a game in which a fair 6-sided die will be rolled. He is all...
Question 3 (15 pts). A gambler plays a game in which a fair 6-sided die will be rolled. He is allowed to bet on two sets of outcomes: A (1,2,3) and B (2,4,5,6). If he bets on A then he wins $1 if one of the numbers in A is rolled and otherwise he loses $1 -let X be the amount won by betting on A (so P(X-1)-P(X1)If he bets on B then he wins $0.50 if a number in...
A fair coin is tossed four times and let x represent the number of heads which...
A fair coin is tossed four times and let x represent the number of heads which comes out a. Find the probability distribution corresponding to the random variable x b. Find the expectation and variance of the probability distribution of the random variable x
You flip a coin 100 times. Let X= the number of heads in 100 flips. Assume...
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1. A fair coin is flipped four times. Find the probability that exactly two of the...
1. A fair coin is flipped four times. Find the probability that exactly two of the flips will turn up as heads. 2. A fair coin is flipped four times. Find the probability that at least two of the flips will turn up as heads. 3. A six-sided dice is rolled twice. Find the probability that the larger of the two rolls was equal to 3. 4. A six-sided dice is rolled twice. Find the probability that the larger of...
3. Consider a coin-die experiment: One flips a fair coin at first. If he gets a head, then he will roll a 6-sided fair die; otherwise, he will roll a 6-sided unfair die, which has probability to get i faces up (i = i, . . . , 6). If one gets a 2 faces up, what is the probability that he got a tail when he flipped the coin? 2.1
Let X equal to the number of heads after 4 flips of a fair coin? Derive the probability mass function for X, and plot it. Also, compute the E[X] of X.
(10 pts) In a game, a player flips a coin three times. The player wins $3 for every head that turns up. The player must pay S5 to play the game. Let the random variable W represent the total winnings after playing the game. (a) Construct the pmf of W (b) Find the expectation and variance of W. (c) Would you play the game? Why or why not?
Question 3 (15 pts). A gambler plays a game in which a fair 6-sided die will be rolled. He is allowed to bet on two sets of outcomes: A (1,2,3) and B (2,4,5,6). If he bets on A then he wins $1 if one of the numbers in A is rolled and otherwise he loses $1 -let X be the amount won by betting on A (so P(X-1)-P(X1)If he bets on B then he wins $0.50 if a number in...
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