The following is based on flipping a fair coin m times, where m is determined bythe roll of an n-sided die (with sides numbered 1, 2,3 ... n). X = num headsAssume the die is fair and n = 6, that is, a 6-sided die.(a) What is the probability mass function of X?(b) What is the expected value of X? Assume the die is biased and n = 3, with the probability of obtaining a 2 more likely than obtaining either a 1 or 3. That is, the probability of obtaining a two is 2/3 and the probability of obtaining a 1 or 3 equally likely. If X = the number of heads obtained.(c) What is the probability mass function of X?(d) What is the expected value of X?(e) Determine the CDF (Cumulative Distribution Function) of X.
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.
The following is based on flipping a fair coin m times, where m is determined by
the roll of an n-sided die (with sides numbered 1, 2,3 ... n). X = num heads
Assume the die is fair and n = 6, that is, a 6-sided die.
(a) What is the
(b) What is the
Assume the die is biased and n = 3, with the probability of obtaining a 2 more likely than obtaining either a 1 or 3. That is, the probability of obtaining a two is 2/3 and the probability of obtaining a 1 or 3 equally likely. If X = the number of heads obtained.
(c) What is the probability mass function of X?
(d) What is the expected value of X?
(e) Determine the CDF (Cumulative Distribution Function) of X.
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