The mode of a discrete random variable X with pmf p(x) is that value x* for which p(x) is largest (the most probable x value). a. Let X ~ Bin(n, p). By considering the ratio b(x + 1; n, p)/b(x; n, p), show that b(x; n, p) increases with x as long as x < np (1 p). Conclude that the mode x* is the integer satisfying (n + 1)p 1 x* (n + 1)p.
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
pmf p(x) is that value x* for which p(x) is largest
(the most
a. Let X ~ Bin(n, p). By considering the ratio
b(x + 1; n, p)/b(x; n, p), show that b(x; n, p)
increases with x as long as x < np (1 p).
Conclude that the mode x* is the integer
satisfying (n + 1)p 1 x* (n + 1)p.
b. Show that if X has a Poisson distribution with
parameter l, the mode is the largest integer
less than l. If l is an integer, show that both
l 1 and l are modes.
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- Recommended textbooks for youA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON
A First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON