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Problem 4 (25 points) Imagine that you flip a coin twice and let X be the...
Suppose you flip a coin 15 times and let x be the discrete random variable of...
Suppose you flip a coin 15 times and let x be the discrete random variable of the number of heads obtained. Use the binomial distribution table to find each of the following probabilities. (A) p(exactly 8 heads)= (b) p(at least one head)= (c) P(at most 3 heads)=
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...
You flip a coin 100 times. Let X= the number of heads in 100 flips. Assume...
You flip a coin 100 times. Let X= the number of heads in 100 flips. Assume we don’t know the probability, p, the coin lands on heads (we don’t know its a fair coin). So, let Y be distributed uniformly on the interval [0,1]. Assume the value of Y = the probability that the coin lands on heads. So, we are given Y is uniformly distributed on [0,1] and X given Y=p is binomially distributed on (100,p). Find E(X) and...
please show formula use not just the amswer, thanks = o 2. Flip a fair coin...
please show formula use not just the amswer, thanks
= o 2. Flip a fair coin twice. Let H: the coin lands on a head; T: the coin lands on a tail. S = {(H, H), (H, T), (T, H), (T, T)} Find: a. P(both are H) 28. b. P(1st is T U 2nd is H) c. P(both are T at least one T)
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...
2. Consider tossing a coin twice. Denote H ="head" and T ="tail" (a) List all outcomes...
2. Consider tossing a coin twice. Denote H ="head" and T ="tail" (a) List all outcomes in the sample space S (b) Let X count the number of heads. List all outcomes in the events Ao = {X = 0}, Ai = {X=1 and A2 {X = 2}. Are all the events Ao,A1,A2 mutually exclusive? Explain. (c) Suppose P(H) = 0.6. Find the probability mass function of X: f(x) = P{X =x} (d) Find the cumulative distribution function of X:...
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...
Question 2 Suppose you have a fair coin (a coin is considered fair if there is...
Question 2 Suppose you have a fair coin (a coin is considered fair if there is an equal probability of being heads or tails after a flip). In other words, each coin flip i follows an independent Bernoulli distribution X Ber(1/2). Define the random variable X, as: i if coin flip i results in heads 10 if coin flip i results in tails a. Suppose you flip the coin n = 10 times. Define the number of heads you observe...
Write a program that simulates the toss of a coin. Whenever a coin is tossed the...
Write a program that simulates the toss of a coin. Whenever a coin is tossed the result will be either a head or tail. Prompt the user as shown by entering an ‘H’ for heads or ‘T’ for tails. Use a loop for input validation of an ‘h’ or ‘t’. Make sure that both an upper case and lower case will be accepted. Have the computer generate a random number. Assign a char variable a (‘h’ ^ ’t’) head or...
1. Multiple choice. Circle all the correct answers a) You flip a coin 100,000 times and...
1. Multiple choice. Circle all the correct answers a) You flip a coin 100,000 times and record the outcome in a Xi 1 if the toss is "Heads" and 0 if its "Tails. The Law of Large Numbers says that: i. ii. It is impossible for the first n flips to all be "Heads" if n is large. With high probability, the share of coin flips that are "Heads" will approximate 50%. The sample mean of X is always 0.5...
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...
please show formula use not just the amswer, thanks
= o 2. Flip a fair coin twice. Let H: the coin lands on a head; T: the coin lands on a tail. S = {(H, H), (H, T), (T, H), (T, T)} Find: a. P(both are H) 28. b. P(1st is T U 2nd is H) c. P(both are T at least one T)
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...
2. Consider tossing a coin twice. Denote H ="head" and T ="tail" (a) List all outcomes in the sample space S (b) Let X count the number of heads. List all outcomes in the events Ao = {X = 0}, Ai = {X=1 and A2 {X = 2}. Are all the events Ao,A1,A2 mutually exclusive? Explain. (c) Suppose P(H) = 0.6. Find the probability mass function of X: f(x) = P{X =x} (d) Find the cumulative distribution function of X:...
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...
Question 2 Suppose you have a fair coin (a coin is considered fair if there is an equal probability of being heads or tails after a flip). In other words, each coin flip i follows an independent Bernoulli distribution X Ber(1/2). Define the random variable X, as: i if coin flip i results in heads 10 if coin flip i results in tails a. Suppose you flip the coin n = 10 times. Define the number of heads you observe...
1. Multiple choice. Circle all the correct answers a) You flip a coin 100,000 times and record the outcome in a Xi 1 if the toss is "Heads" and 0 if its "Tails. The Law of Large Numbers says that: i. ii. It is impossible for the first n flips to all be "Heads" if n is large. With high probability, the share of coin flips that are "Heads" will approximate 50%. The sample mean of X is always 0.5...
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