![Problem 4, 5 p. ] (in prepation to the binomial model) Consider tossing a coin n times where n 1 is fixed. Assume that the probability of occurring of heads is p(0< p1), and the probability of occurring of tails is q1-p and the outcomes of single tosses are independent of each other. Describe the sample space Ω of that experiment (all possible outcomes) and how the corresponding probability function P on Ω looks like. In other words, prescribe P to any elementary outcome of the experiment.](http://img.homeworklib.com/questions/0215f040-3027-11eb-bb33-3533733d6ed2.png?x-oss-process=image/resize,w_560)
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Problem 4, 5 p. ] (in prepation to the binomial model) Consider tossing a coin n...
4. Let 210,1,2) be the outcome space in a model for tossing a coin twice and...
4. Let 210,1,2) be the outcome space in a model for tossing a coin twice and observing the total number of heads. Say if the following events can be represented as subsets of Ω. If you say "yes," provide the subset; if you say "no," explain why: a) the coin does not land heads both times; bon one of the tosses the coin lands heads, and on the other toss it lands tails; Section 1.3. Distributions 31 C) on the...
3. (PMF – 8 points) Consider a sequence of independent trials of fair coin tossing. Let...
3. (PMF – 8 points) Consider a sequence of independent trials of fair coin tossing. Let X denote a random variable that indicates the number of coin tosses you tried until you get heads for the first time and let y denote a random variable that indicates the number of coin tosses you tried until you get tails for the first time. For example, X = 1 and Y = 2 if you get heads on the first try and...
An experiment consists of tossing an unfair coin (49% chance of landing on heads) a specified...
An experiment consists of tossing an unfair coin (49% chance of landing on heads) a specified number of times and recording the outcomes. (a) What is the probability that the first head will occur on the second trial? (Use 4 decimal places.) Does this probability change if we toss the coin three times? What if we toss the coin four times? The probability changes if we toss the coin four times, but does not change if we toss the coin...
please show details 4. Let S2 (0, 1,2) be the outcome space in a model for...
please show details
4. Let S2 (0, 1,2) be the outcome space in a model for tossing a coin twice and observing the total number of heads. Say if the following events can be represented as subsets of 2. If you say "yes," provide the subset; if you say "no," explain why a) the coin does not land heads both times; b) on one of the tosses the coin lands heads, and on the other toss it lands tails; Section...
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...
An experiment consists of tossing an unfair coin (53% chance of landing on heads) a specified...
An experiment consists of tossing an unfair coin (53% chance of landing on heads) a specified number of times and recording the outcomes. (a) What is the probability that the first head will occur on the second trial? (Use 4 decimal places.) Does this probability change if we toss the coin three times? What if we toss the coin four times? The probability changes if we toss the coin three times, but does not change if we toss the coin...
Alice has two coins. The probability of Heads for the first coin is 1/4, and the...
Alice has two coins. The probability of Heads for the first coin is 1/4, and the probability of Heads for the second is 3/4. Other than this difference, the coins are indistinguishable. Alice chooses one of the coins at random and sends it to Bob. The random selection used by Alice to pick the coin to send to Bob is such that the first coin has a probability p of being selected. Assume that 0<p<1. Bob tries to guess which...
The next four questions (5 to 8) refer to the following: An unfair coin is tossed...
The next four questions (5 to 8) refer to the following: An unfair coin is tossed three times. For each toss, the probability that the coin comes up heads is 0.6 and the probability that the coin comes up tails is 0.4. If we let X be the number of coin tosses that come up heads, observe that the possible values of Xare 0, 1, 2, and 3. Find the probability distribution of X. Hint: the problem can be solved...
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...
4. Let 210,1,2) be the outcome space in a model for tossing a coin twice and observing the total number of heads. Say if the following events can be represented as subsets of Ω. If you say "yes," provide the subset; if you say "no," explain why: a) the coin does not land heads both times; bon one of the tosses the coin lands heads, and on the other toss it lands tails; Section 1.3. Distributions 31 C) on the...
3. (PMF – 8 points) Consider a sequence of independent trials of fair coin tossing. Let X denote a random variable that indicates the number of coin tosses you tried until you get heads for the first time and let y denote a random variable that indicates the number of coin tosses you tried until you get tails for the first time. For example, X = 1 and Y = 2 if you get heads on the first try and...
please show details
4. Let S2 (0, 1,2) be the outcome space in a model for tossing a coin twice and observing the total number of heads. Say if the following events can be represented as subsets of 2. If you say "yes," provide the subset; if you say "no," explain why a) the coin does not land heads both times; b) on one of the tosses the coin lands heads, and on the other toss it lands tails; Section...
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...
The next four questions (5 to 8) refer to the following: An unfair coin is tossed three times. For each toss, the probability that the coin comes up heads is 0.6 and the probability that the coin comes up tails is 0.4. If we let X be the number of coin tosses that come up heads, observe that the possible values of Xare 0, 1, 2, and 3. Find the probability distribution of X. Hint: the problem can be solved...
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...
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