Let N be a binomial random variable with p = 0.2 and n = 10. We...
Let N be a binomial random variable with p = 0.2 and n = 10. We roll a fair die N times, let X be the number of times we roll the number 1. Find the joint probability mass function of N and X.
Homework Answers
Consider a binomial random variable with n = 5 and p = 0.7
4. Consider a binomial random variable with n = 5 and p = 0.7. Let x be the number of successes in the sample. Evaluate the probability. (Round your answer to three decimal places.) 5. Let x be a binomial random variable with n = 8, p = 0.2. Find the following value. 6. Let x be a binomial random variable with n = 8, p = 0.3. Find the following value. (Round your answer to three decimal places.)
Let X be a binomial random variable with p 0.3 and n 10. Calculate the following...
Let X be a binomial random variable with p 0.3 and n 10. Calculate the following probabilities from the binomial probability mass function. Round your answers to four decimal places (e.g. 98.7654). P(X> 8)
Let X be a discrete random variable with 1 P(X = 1) = P(X = 2)...
Let X be a discrete random variable with 1 P(X = 1) = P(X = 2) = P(X = 3) = P(X= 4) = Then given X = x, we roll a fair 4-sided die 3 times. (The 4-sided die is equally likely to come up a 1, 2, 3, or 4). Let y be the number of times we roll a 1. (a) Find E[Y|X]. Hint: Remember E[Y | X] is a random variable, so X will be part...
Let N be a binomial random variable with n = 2 trials and success probability p...
Let N be a binomial random variable with n = 2 trials and success probability p = 0.5. Let X and Y be uniform random variables on [0, 1] and that X, Y, N are mutually independent. Find the probability density function for Z = NXY.
Problem 5. Let X be a binomial random variable with parameters n and p. Suppose that...
Problem 5. Let X be a binomial random variable with parameters n and p. Suppose that we want to generate a random variable Y whose probability mass function is the same as the conditional mass function of X given X-k, for some k-n. Let a = P(X-k), and suppose that the value of a has been computed (a) Give the inverse transform method for generating Y. (b) Give a second method for generating Y (c) For what values of a,...
Let X be a binomial random variable with n = 5 and p = 0.30 Use...
Let X be a binomial random variable with n = 5 and p = 0.30 Use the Binomial Tables to obtain the correct probability distribution Find each probability. 1) P(X = 5) 2) P(X ?= 1)
Let X be a binomial random variable with p four decimal places (e.g. 98.7654) 10. Calculate...
Let X be a binomial random variable with p four decimal places (e.g. 98.7654) 10. Calculate the following probabilities from the binomial probability mass function. Round your answers to 0.7 and n
Let X be a discrete random variable with P(X = 1) = 1 4 1 P(X...
Let X be a discrete random variable with P(X = 1) = 1 4 1 P(X = 2) = 8 1 P(X = 3) = 2 P(X = 4) = 8 Then given X = x, we roll a fair 4-sided die x times. (The 4- sided die is equally likely to come up a 1, 2, 3, or 4). Let y be the number of times we roll a 1. (a) Find E[Y| X]. Hint: Remember E|Y|X] is a...
A. Let X be a binomial random variable with n = 74 and p = .6....
A. Let X be a binomial random variable with n = 74 and p = .6. Use the normal approximation to the binomial to find: (i) P(X ≤ 50) (iii) P(40 ≤ X ≤ 50) (v) P(X = 43) (ii) P(X ≥ 40) (iv) P(42 ≤ X < 49) B. Each time a roulette wheel is spun, there are 38 possible outcomes, 18 red, 18 black, and two green. Suppose that you ALWAYS bet "black". (i) Suppose the roulette wheel...
Problem 4 (10 points). Let X be a binomial random variable with parameters n = 15...
Problem 4 (10 points). Let X be a binomial random variable with parameters n = 15 and p. (1) If p = 0.30, Find E(X + (n - X)). [Note that n-X is the number of failures). (2) Find p such that P(X = 6) is most probable. In other words, please find p = po such that P(X = 6) achieves at the maximum as a function of p at p = Po
4. Consider a binomial random variable with n = 5 and p = 0.7. Let x be the number of successes in the sample. Evaluate the probability. (Round your answer to three decimal places.) 5. Let x be a binomial random variable with n = 8, p = 0.2. Find the following value. 6. Let x be a binomial random variable with n = 8, p = 0.3. Find the following value. (Round your answer to three decimal places.)
Let X be a binomial random variable with p 0.3 and n 10. Calculate the following probabilities from the binomial probability mass function. Round your answers to four decimal places (e.g. 98.7654). P(X> 8)
Let X be a discrete random variable with 1 P(X = 1) = P(X = 2) = P(X = 3) = P(X= 4) = Then given X = x, we roll a fair 4-sided die 3 times. (The 4-sided die is equally likely to come up a 1, 2, 3, or 4). Let y be the number of times we roll a 1. (a) Find E[Y|X]. Hint: Remember E[Y | X] is a random variable, so X will be part...
Problem 5. Let X be a binomial random variable with parameters n and p. Suppose that we want to generate a random variable Y whose probability mass function is the same as the conditional mass function of X given X-k, for some k-n. Let a = P(X-k), and suppose that the value of a has been computed (a) Give the inverse transform method for generating Y. (b) Give a second method for generating Y (c) For what values of a,...
Let X be a binomial random variable with p four decimal places (e.g. 98.7654) 10. Calculate the following probabilities from the binomial probability mass function. Round your answers to 0.7 and n
Let X be a discrete random variable with P(X = 1) = 1 4 1 P(X = 2) = 8 1 P(X = 3) = 2 P(X = 4) = 8 Then given X = x, we roll a fair 4-sided die x times. (The 4- sided die is equally likely to come up a 1, 2, 3, or 4). Let y be the number of times we roll a 1. (a) Find E[Y| X]. Hint: Remember E|Y|X] is a...
Problem 4 (10 points). Let X be a binomial random variable with parameters n = 15 and p. (1) If p = 0.30, Find E(X + (n - X)). [Note that n-X is the number of failures). (2) Find p such that P(X = 6) is most probable. In other words, please find p = po such that P(X = 6) achieves at the maximum as a function of p at p = Po
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