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of a fair coin. Also use the binomial formula and compare the two probabilities. For the...
We flip a coin. If it is heads we roll a four sided die with sides...
We flip a coin. If it is heads we roll a four sided die with sides numbered from 1 to 4. If it is tails, we roll a six sided die with sides numbered from 1 to 6. We let X be the number rolled. (a) What is the expectation of X? (b) What is the variance of X? (c) What is the standard deviation of X? We draw cards one by one and with replacement from a standard deck...
3) We roll 2 fair dice. a) Find the probabilities of getting each possible sum (i.e....
3) We roll 2 fair dice. a) Find the probabilities of getting each possible sum (i.e. find Pr(2), Pr(3), . Pr(12) ) b) Find the probability of getting a sum of 3 or 4 (i.e.find Pr(3 or 4)) c) Find the probability we roll doubles (both dice show the same value). d) Find the probability that we roll a sum of 8 or doubles (both dice show the same value). e) Is it more likely that we get a sum...
We roll two fair 6-sided dice. (1) What is the probability that at least one die...
We roll two fair 6-sided dice. (1) What is the probability that at least one die roll is 6? (2) Given that two two dice land on different numbers, what is the conditional probability that at least one die roll is a 6? Thint] You may use the graphical approach (Lecture 5 slide 11-12) to help you solve the problem. Problem 4. (8 points) We deal from a well-shuffled 52-card deck. What is the probability that the 13th card is...
Assume a fair coin is flipped 3 times. Probability of getting heads is .5..Use the normal...
Assume a fair coin is flipped 3 times. Probability of getting heads is .5..Use the normal approximation method (and relevant standard normal table) to solve by hand for the probability of obtaining 2 or more successes of getting heads in this situation. Show your work.
A fair quarter is flipped three times. For each of the following probabilities, use the formula...
A fair quarter is flipped three times. For each of the following probabilities, use the formula for the binomial distribution and a calculator to compute the requested probability. Next, look up the probability in the binomial probability distribution table. (Enter your answers to three decimal places.) (a) Find the probability of getting exactly three heads. (b) Find the probability of getting exactly two heads. (c) Find the probability of getting two or more heads. (d) Find the probability of getting...
A fair quarter is flipped 4 times. For each of the following probabilities, use the binomial...
A fair quarter is flipped 4 times. For each of the following probabilities, use the binomial distribution table to compute the requested probability. a.) Find the probability of getting exactly 2 tails. b.) Find the probability of getting three or more tails. c.) Find the probability of getting no heads. d.) Find the probability of getting exactly 1 head. e.) Find the probability of getting exactly 4 tails
Consider the following discrete random variables W is the number of times heads is observed when a fair coin is tossed...
Consider the following discrete random variables W is the number of times heads is observed when a fair coin is tossed 10 times. X is the number of red balls drawn when 10 balls are drawn without replacement from an urn containing 50 red balls and 30 green balls. Y is the number of hearts received when a 10-card hand is dealt from a standard deck. Z is the number of hearts drawn when 1 card is drawn at random...
1. We roll two fair 6-sided dice. Compute the probabilities of the following events. (a) The...
1. We roll two fair 6-sided dice. Compute the probabilities of the following events. (a) The sum is at most 6. (b) The sum is more than 6. (c) The sum is at most 6 and at least one die is a 4. 2. Consider the letters a,b,c. Suppose we draw 2 of the letters at random (allowing for repetition). Assume order matters. That is, ab is not the same as ba: Let A : The 2 letters are distinct....
find correlation using covariance ? 1. (No key parameter) We flip a fair coin with the...
find correlation using covariance ?
1. (No key parameter) We flip a fair coin with the outcomes X = +1 for heads, and X = -1 for tails, we also toss a fair die with the outcome Y E (1,2,3,4,5,6) the number of dots on the face up. Find the correlation of the random variables E[XY] =? Use the covariance equation to prove your answer. ccc -0.2v .
You will receive a prize if both a fair coin lands "heads" AND a fair die...
You will receive a prize if both a fair coin lands "heads" AND a fair die lands "6". After the coin is flipped and the die is rolled you ask if AT LEAST ONE of these events has occurred and you are told "yes." Formally calculate the probability of you winning the prize, whilst answering these questions in each step of your answer i. Specify the joint distribution, ?(?,?,?,?), in terms of its constituent conditional distributions ii. Specify the full...
We flip a coin. If it is heads we roll a four sided die with sides numbered from 1 to 4. If it is tails, we roll a six sided die with sides numbered from 1 to 6. We let X be the number rolled. (a) What is the expectation of X? (b) What is the variance of X? (c) What is the standard deviation of X? We draw cards one by one and with replacement from a standard deck...
3) We roll 2 fair dice. a) Find the probabilities of getting each possible sum (i.e. find Pr(2), Pr(3), . Pr(12) ) b) Find the probability of getting a sum of 3 or 4 (i.e.find Pr(3 or 4)) c) Find the probability we roll doubles (both dice show the same value). d) Find the probability that we roll a sum of 8 or doubles (both dice show the same value). e) Is it more likely that we get a sum...
We roll two fair 6-sided dice. (1) What is the probability that at least one die roll is 6? (2) Given that two two dice land on different numbers, what is the conditional probability that at least one die roll is a 6? Thint] You may use the graphical approach (Lecture 5 slide 11-12) to help you solve the problem. Problem 4. (8 points) We deal from a well-shuffled 52-card deck. What is the probability that the 13th card is...
find correlation using covariance ?
1. (No key parameter) We flip a fair coin with the outcomes X = +1 for heads, and X = -1 for tails, we also toss a fair die with the outcome Y E (1,2,3,4,5,6) the number of dots on the face up. Find the correlation of the random variables E[XY] =? Use the covariance equation to prove your answer. ccc -0.2v .
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