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7. Suppose that an experiment has two outcomes 0 or 1 (such as flipping a coin). Suppose that independent experimen...
Suppose you run n independent simulations of an experiment, and suppose that on each single simulation...
Suppose you run n independent simulations of an experiment, and suppose that on each single simulation the chance that the experiment is a success is p. Let X be the proportion of successful experiments among the n experiments in your simulation. You can assume n is sufficiently big to apply CLT. Fill in the blank with a function of n and p, and explain your answer: P(X ∈ p± ___________) ≈ 0.95
all questions please 1. (a) What is the sample space S for flipping a coin until...
all questions please
1. (a) What is the sample space S for flipping a coin until you get a head or 4 consecutive tails? Write down your sample space by listing the elements (b) An experiment involves tossing a pair of dice, one green and one red, recording the numbers that come up. These are special dice. Each die has only 5 sides and are labeled with the numbers 1, 2, 3, 4, 5. Let r be the outcome on...
1. (a) What is the sample space S for flipping a coin until you get a...
1. (a) What is the sample space S for flipping a coin until you get a head or 4 consecutive tails? Write down your sample space by listing the elements. (b) An experiment involves tossing a pair of dice, one green and one red, recording the numbers that come up. These are special dice. Each die has only 5 sides and are labeled with the numbers 1, 2, 3, 4, 5. Let r be the outcome on the green die...
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...
Suppose there are n independent trials of an experiment with k>3 mutually exclusive outcomes, where pi...
Suppose there are n independent trials of an experiment with k>3 mutually exclusive outcomes, where pi represents the probability of observing the ith outcome. What would be the formula of an expected count in this situation? Choose the correct answer below. A. The expected counts for each possible outcome are given by Ei=npi. B. The expected counts for each possible outcome are given by Ei=n/pi (n over pi) C. The expected counts for each possible outcome are given by Ei=pi....
You just picked up a coin and is wondering if the coin is truly unbiased. To...
You just picked up a coin and is wondering if the coin is truly unbiased. To determine if this coin is unbiased, you decide to do an experiment by flipping this coin 100 times and record how many times it returns head. Let us say this is flipping experiment No.1, and its result is the no. of heads. Then you decide to repeat this flipping experiment 999 more times (for a total of 1000 experiments, in each experiment you flip...
Suppose you plan flipping a coin twice where the probability p of heads has the density...
Suppose you plan flipping a coin twice where the probability p of heads has the density function f(p) = 6p(1 - p), 0 < p < 1. Let Y denote the number of heads of this “random” coin. Y given a value of p is Binomial with n = 2 and probability of success p. a. Write down the joint density of Y and p. b. Find P(Y = 2). c. If Y = 2, then find the probability that...
Problem 6 7. Part 1-4 (10pts)A coin has two faces Head and Tail. (1) (2pts)]lf you...
Problem 6
7. Part 1-4
(10pts)A coin has two faces Head and Tail. (1) (2pts)]lf you toss the coin once, and record the up-face value, what is the sample space? 6. (2) (2pts)lf you toss the coin once, what is the probability that up-face is Tail? What is the probability that up-face is Head? (3) (5ps)lf you toss the coin three times, and record the up-face value for each toss. One of the possible outcome is (Head, Head, Head). By...
Problem 4, 5 p. ] (in prepation to the binomial model) Consider tossing a coin n...
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...
Problem 5 - Rare outcomes and data set size Here we will be concerned with a biased coin for whic...
Problem 5 - Rare outcomes and data set size Here we will be concerned with a biased coin for which outcome 1 has a very low probability, i.e 0 < θι < 6o << 1. Assume our experiment consists of n independent tosses of this coin. 1. What is the probability po P(n1 0) that the outcome sequence contains no 1's? Write the answer as a function of θ| and n 2. What is the probability pi P(n1-1) that the...
all questions please
1. (a) What is the sample space S for flipping a coin until you get a head or 4 consecutive tails? Write down your sample space by listing the elements (b) An experiment involves tossing a pair of dice, one green and one red, recording the numbers that come up. These are special dice. Each die has only 5 sides and are labeled with the numbers 1, 2, 3, 4, 5. Let r be the outcome on...
1. (a) What is the sample space S for flipping a coin until you get a head or 4 consecutive tails? Write down your sample space by listing the elements. (b) An experiment involves tossing a pair of dice, one green and one red, recording the numbers that come up. These are special dice. Each die has only 5 sides and are labeled with the numbers 1, 2, 3, 4, 5. Let r be the outcome on the green die...
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...
Suppose you plan flipping a coin twice where the probability p of heads has the density function f(p) = 6p(1 - p), 0 < p < 1. Let Y denote the number of heads of this “random” coin. Y given a value of p is Binomial with n = 2 and probability of success p. a. Write down the joint density of Y and p. b. Find P(Y = 2). c. If Y = 2, then find the probability that...
Problem 6
7. Part 1-4
(10pts)A coin has two faces Head and Tail. (1) (2pts)]lf you toss the coin once, and record the up-face value, what is the sample space? 6. (2) (2pts)lf you toss the coin once, what is the probability that up-face is Tail? What is the probability that up-face is Head? (3) (5ps)lf you toss the coin three times, and record the up-face value for each toss. One of the possible outcome is (Head, Head, Head). By...
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...
Problem 5 - Rare outcomes and data set size Here we will be concerned with a biased coin for which outcome 1 has a very low probability, i.e 0 < θι < 6o << 1. Assume our experiment consists of n independent tosses of this coin. 1. What is the probability po P(n1 0) that the outcome sequence contains no 1's? Write the answer as a function of θ| and n 2. What is the probability pi P(n1-1) that the...
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