Suppose a discrete random variable X assumes the value 3/2 with probability 0.5 and assumes the value 1/2 with probability 0.5. a). Calculate the expected value and variance of X. b). Suppose that X1, X2, and X3 are three independent random variables with the same distribution as X.What is the expected value of the sum X1 + X2 + X3? The product X1X2X3? Problem 6: Suppose that you have one hundred independent instances of X as defined in Problem 5. Use Markov’s inequality to prove that the probability that the product of all one hundred instances exceeds 50 is less than 1/50.
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
Please only answer problem 6:
Problem 5: Suppose a discrete random variable X assumes the value 3/2 with
a). Calculate the
b). Suppose that X1, X2, and X3 are three independent random variables with the same distribution as X.What is the expected value of the sum X1 + X2 + X3? The product X1X2X3?
Problem 6: Suppose that you have one hundred independent instances of X as defined in Problem 5. Use Markov’s inequality to prove that the probability that the product of all one hundred instances exceeds 50 is less than 1/50.
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