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Consider a random variable X that can take on only two values, 0 and 1, with equal probability. a) Show that E (X) = 1/2 and V (X) = 1/4. Also, obtain a bar plot for the probability distribution of X. (This visualization might help you in the next part) b) Come up with another random variable, say Y, such that E (Y) = 1/2 and V (Y) = 1/4 but its distribution is not the same as X. Also, show its prob- ability distribution on a bar chart. (You are free to choose the number of possible outcomes, their values and probabilities however you want.)

Consider a random variable X that can take on only two values, 0 and 1, with equal probability. a) Show that E (X) = 1/2 and V (X) = 1/4. Also, obtain a bar plot for the probability distribution of X. (This visualization might help you in the next part) b) Come up with another random variable, say Y, such that E (Y) = 1/2 and V (Y) = 1/4 but its distribution is not the same as X. Also, show its prob- ability distribution on a bar chart. (You are free to choose the number of possible outcomes, their values and probabilities however you want.)

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Consider a random variable X that can take on only two values, 0 and 1, with equal probability. a) Show that E (X) = 1/2 and V (X) = 1/4. Also, obtain a bar plot for the probability distribution of X. (This visualization might help you in the next part) b) Come up with another random variable, say Y, such that E (Y) = 1/2 and V (Y) = 1/4 but its distribution is not the same as X. Also, show its prob- ability distribution on a bar chart. (You are free to choose the number of possible outcomes, their values and probabilities however you want.)
Transcribed Image Text:Consider a random variable X that can take on only two values, 0 and 1, with equal probability. a) Show that E (X) = 1/2 and V (X) = 1/4. Also, obtain a bar plot for the probability distribution of X. (This visualization might help you in the next part) b) Come up with another random variable, say Y, such that E (Y) = 1/2 and V (Y) = 1/4 but its distribution is not the same as X. Also, show its prob- ability distribution on a bar chart. (You are free to choose the number of possible outcomes, their values and probabilities however you want.)
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