A certain hurricane database extends back to​ 1851, recording among other data the number of major hurricanes​ (measuring at least a Category​ 3) striking a certain region per year. The following table provides a probability distribution for the number of major​ hurricanes, Y, for a randomly selected year between 1851 and 2012.      y ​P(Y=​y)   y ​P(Y=​y)     0 0.186   5 0.041     1 0.252   6 0.027     2 0.246   7 0.011     3 0.094   8 0.104     4 0.039       f. Use the special addition rule and the probability distribution to determine the probability that the year had between 3 and 5 major​ hurricanes, inclusive.   The probability is_______   The table below shows the probability distribution of the random variable X. x 1 2 3   ​P(X=​x) 0.3 0.1 0.6 b. Obtain the standard deviation σ of the random variable. σ=________   The random variable X is the crew size of a randomly selected shuttle mission. Its probability distribution is shown below. Complete parts a through c.   x 2 4 5 6 7 8   ​P(X=​x) 0.035 0.032 0.324 0.168 0.435 0.006   a. Find and interpret the mean of the random variable. μ=______

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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.