8. IThe probability mass function of a random variable J is given as where J = {-1,0, 1} fO) = {7 8' 0, a. Is the probability distribution function valid? Prove your answer elsewhere b. Calculate for the probability of x<½ c. Draw the histogram of the probability mass function

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A: Given the joint probability distribution function of two random variables X and Y as…

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A: Hey there! Thank you for posting the question. However, since your question has more than 3…

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A:

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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.