A random experiment is to roll a dice. The corresponding random variable X is defined as follows.
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A random experiment is to roll a dice. The corresponding random variable X is defined
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as follows. X = i when a number i appears. i can be 1,2,3,4,5,6. The dice is fair. (a) Draw probability mass function. (b) Draw distribution function(i.e., Cumulative distribution function) (e) What is the expectation of X? 2. A random variable y follows a uniform distribution on [0, 1], It means that the random variable Y takes any value between 0 to 1. (a) What is the probability density function of Y, fy (y)? (b) What is the distribution function of T, Fy(y) = Pr[Y ≤y]? (e) What is the expectation of Y? (d) What is the 40 percentile of Y? 3. Suppose that there are two discrete random variables, W and Z Table 1: A joint probability of W and Z Z=0 Z=1 W = 0 1/12 1/6 W = 1 2/3 1/12 (a) What is the marginal probability of W?(that is, compute Pr[W= w] for all w = 0, 1.) as follows. X = i when a number i appears. i can be 1,2,3,4,5,6. The dice is fair. (a) Draw probability mass function. (b) Draw distribution function(i.e., Cumulative distribution function) (e) What is the expectation of X? 2. A random variable y follows a uniform distribution on [0, 1], It means that the random variable Y takes any value between 0 to 1. (a) What is the probability density function of Y, fy (y)? (b) What is the distribution function of T, Fy(y) = Pr[Y ≤y]? (e) What is the expectation of Y? (d) What is the 40 percentile of Y? 3. Suppose that there are two discrete random variables, W and Z Table 1: A joint probability of W and Z Z=0 Z=1 W = 0 1/12 1/6 W = 1 2/3 1/12 (a) What is the marginal probability of W?(that is, compute Pr[W= w] for all w = 0, 1.)
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Answer rating: 100% (QA)
1 Random variable X when rolling a fair sixsided dice a Probability Mass Function PMF The PMF gives the probabilities associated with each possible va... View the full answer
Related Book For
Introduction to Probability
ISBN: 978-0716771098
1st edition
Authors: Mark Daniel Ward, Ellen Gundlach
Posted Date:
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