1. A fair coin is flipped until three heads are observed in a row. Let denote...
1. A fair coin is flipped until three heads are observed in a row. Let denote the number of trials in this experiment. [This is a simple model of some procedures in acceptance control].
b) Find p(x) for the first five values of X
c) Make an estimate of EX. Hint: use geometric rv related to X.
Homework Answers
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1. A fair coin is flipped until three heads are observed in a
row. Let denote...
A fair coin is flipped independently until the first Heads is observed. Let the random variable...
A fair coin is flipped independently until the first Heads is observed. Let the random variable K be the number of tosses until the first Heads is observed plus 1. For example, if we see TTTHTH, then K = 5. For k 1, 2, , K, let Xk be a continuous random variable that is uniform over the interval [0, 5]. The Xk are independent of one another and of the coin flips. LetX = Σ i Xo Find the...
Problem 3. A fair coin is flipped until five heads are observed. Find the probability mass...
Problem 3. A fair coin is flipped until five heads are observed. Find the probability mass function and the expectation of the number of tails shown until then.
6. A fair coin is flipped repeatedly until 50 heads are observed. What is the probability...
6. A fair coin is flipped repeatedly until 50 heads are observed. What is the probability that at least 80 flips are necessary? (You may calculate an approximate answer.)
Exercise 8.52. A fair coin is flipped 30 times. LetX denote the number of heads among...
Exercise 8.52. A fair coin is flipped 30 times. LetX denote the number of heads among the first 20 coin flips and Y denote the number of heads among the last 20 coin flips. Compute the correlation coefficient of X and I.
A fair coin is tossed five times. Let X denote the number of heads. Find the...
A fair coin is tossed five times. Let X denote the number of heads. Find the variance of X.
18. A fair coin is flipped multiple times until it lands on heads. If the probability...
18. A fair coin is flipped multiple times until it lands on heads. If the probability of landing on ( point) heads is 50%, what is the probability of first landing on heads on the fourth attempt? 00.625 0.500 00.412 00.382
7. A fair coin is flipped multiple times until it lands on heads. If the probability...
7. A fair coin is flipped multiple times until it lands on heads. If the probability of landing on ( point) heads is 50%, what is the probability of first landing on heads on the third attempt? ○ 0,096 0.107 o 0.121 00.125
4. Toss a fair coin 6 times and let X denote the number of heads that...
4. Toss a fair coin 6 times and let X denote the number of heads
that appear. Compute P(X ≤ 4). If the coin has probability p of
landing heads, compute P(X ≤ 3)
4. Toss a fair coin 6 times and let X denote the number of heads that appear. Compute P(X 4). If the coin has probability p of landing heads, compute P(X < 3).
Suppose you just flipped a fair coin 8 times in a row and you got heads...
Suppose you just flipped a fair coin 8 times in a row and you got heads each time! What is the probability that the next coin flip will result in a heads? Write answer as a decimal and round to 1 place after the decimal point.
A fair coin is flipped until the first head appears. Let X= the total number of times the coin is...
A fair coin is flipped until the first head appears. Let X= the total number of times the coin is flipped. Find E(x). Hint:if the first flip is tails, this "game" restarts.
A fair coin is flipped independently until the first Heads is observed. Let the random variable K be the number of tosses until the first Heads is observed plus 1. For example, if we see TTTHTH, then K = 5. For k 1, 2, , K, let Xk be a continuous random variable that is uniform over the interval [0, 5]. The Xk are independent of one another and of the coin flips. LetX = Σ i Xo Find the...
Problem 3. A fair coin is flipped until five heads are observed. Find the probability mass function and the expectation of the number of tails shown until then.
6. A fair coin is flipped repeatedly until 50 heads are observed. What is the probability that at least 80 flips are necessary? (You may calculate an approximate answer.)
Exercise 8.52. A fair coin is flipped 30 times. LetX denote the number of heads among the first 20 coin flips and Y denote the number of heads among the last 20 coin flips. Compute the correlation coefficient of X and I.
18. A fair coin is flipped multiple times until it lands on heads. If the probability of landing on ( point) heads is 50%, what is the probability of first landing on heads on the fourth attempt? 00.625 0.500 00.412 00.382
7. A fair coin is flipped multiple times until it lands on heads. If the probability of landing on ( point) heads is 50%, what is the probability of first landing on heads on the third attempt? ○ 0,096 0.107 o 0.121 00.125
4. Toss a fair coin 6 times and let X denote the number of heads
that appear. Compute P(X ≤ 4). If the coin has probability p of
landing heads, compute P(X ≤ 3)
4. Toss a fair coin 6 times and let X denote the number of heads that appear. Compute P(X 4). If the coin has probability p of landing heads, compute P(X < 3).
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