1. Three fair coins are flipped independently. Let X be the number of heads among the...
1. Three fair coins are flipped independently. Let X be the number of heads among the three coins
(d) Compute E[X] and Var(X).
2. Suppose that we have a set of temperature measurements in degree Celsius, with mean 32(◦C) and variance 25(◦C)2. What is the variance of same set of measurements in degree Fahrenheit? The formula connecting degree Celsius and degree Fahrenheit is: Y (◦F) = 1.8X(◦C) + 32.
(A) 45(◦F) (B) 81(◦F) (C) 45(◦F)2 (D) 81(◦F)2
Homework Answers
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1. Three fair coins are flipped independently. Let X be the
number of heads among the...
please show all work 2. (20 points) Three fair coins are flipped independently. Let X be...
please show all work
2. (20 points) Three fair coins are flipped independently. Let X be the number of heads among the three coins. (a) Write down all possible values that X can take. (b) Construct the probability mass function of X. (c) What is the probability that we observe two or more heads. (i.e., P(X > 2)) (d) Compute E(X) and Var(X).
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...
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.
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.
Five fair coins were flipped. Part (a): How many possible outcomes there will be, if the...
Five fair coins were flipped. Part (a): How many possible outcomes there will be, if the order of coins are considered? Part (b): How many possible outcomes with exactly 3 heads? Part (c): What is the probability of getting a result with exactly 3 heads? (Round to 4 decimal places, if needed.) Part (d): What is the probability of getting a result with less than 2 head? (Round to 4 decimal places, if needed.)
Five fair coins will be flipped; each coin is a different color. You may not use...
Five fair coins will be flipped; each coin is a different color. You may not use a calculator, but you may also leave your answer as a sum, product, and/or quotient of integers. You do not need to simplify. The events E, F, and G are defined as follows: E: There are an even number heads, G: All five coins come up heads, F: The total number of heads is > 4, H: The first coin comes up heads. Answer...
Five fair coins will be flipped; each coin is a different color. You may not use...
Five fair coins will be flipped; each coin is a different color. You may not use a calculator, but you may also leave your answer as a sum, product, and/or quotient of integers. You do not need to simplify. The events E, F, and G are defined as follows: E: There are an even number heads, F: The total number of heads is > 4, G: All five coins come up heads, H: The first coin comes up heads. Answer...
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...
Graph using Rstudio: 1. Suppose four distinct, fair coins are tossed. Let the random variable X...
Graph using Rstudio: 1. Suppose four distinct, fair coins are tossed. Let the random variable X be the number of heads. Write the probability mass function f(x). Graph f(x). 2. For the probability mass function obtained, what is the cumulative distribution function F(x)? Graph F(x). 3. Find the mean (expected value) of the random variable X given in part 1 4. Find the variance of the random variable X given in part 1.
Suppose you flip three fair, mutually independent coins. Define the following events: Let A be the...
Suppose you flip three fair, mutually independent coins. Define the following events: Let A be the event that the first coin is heads. Let B be the event that the second coin is heads. Let C be the event that the third coin is heads. Let D be the event that an even number of coins are heads. Determine the probability space for this experiment (build the probability tree). Using the probability tree, find the probability of each of the...
please show all work
2. (20 points) Three fair coins are flipped independently. Let X be the number of heads among the three coins. (a) Write down all possible values that X can take. (b) Construct the probability mass function of X. (c) What is the probability that we observe two or more heads. (i.e., P(X > 2)) (d) Compute E(X) and Var(X).
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...
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.
Five fair coins will be flipped; each coin is a different color. You may not use a calculator, but you may also leave your answer as a sum, product, and/or quotient of integers. You do not need to simplify. The events E, F, and G are defined as follows: E: There are an even number heads, G: All five coins come up heads, F: The total number of heads is > 4, H: The first coin comes up heads. Answer...
Five fair coins will be flipped; each coin is a different color. You may not use a calculator, but you may also leave your answer as a sum, product, and/or quotient of integers. You do not need to simplify. The events E, F, and G are defined as follows: E: There are an even number heads, F: The total number of heads is > 4, G: All five coins come up heads, H: The first coin comes up heads. Answer...
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