The N Candidates for a Store Manager Have Been Ranked $$p ( x ) = \left\{ \begin{array} { l l } 1 / n & x = 1,2,3 \ldots , n \\0 & \text { otherwise }\end{array} \right.$$

question 14

Essay

The n candidates for a store manager have been ranked 1,2,3,…,n. Let X = the rank of a randomly selected candidate, so that X has pmf $$p ( x ) = \left\{ \begin{array} { l l } 1 / n & x = 1,2,3 \ldots , n \\0 & \text { otherwise }\end{array} \right.$$ (this is called the discrete uniform distribution). Compute E(X) and V(X) using the shortcut formula. [Hint: The sum of the first n positive integers is n(n + 1)/2, whereas the sum of their squares is n(n + 1)(2n + 1)/6.]

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Definitions:

Police Officers

Law enforcement members responsible for maintaining public order, enforcing laws, and preventing, detecting, and investigating criminal activities.

Whiskers

In a box plot, the lines that extend from the quartiles to the furthest data points within a reasonable range, representing the spread of the bulk of the data.

Box Plot

A graphical representation of a dataset that shows the distribution's minimum, first quartile, median, third quartile, and maximum.

Interquartile Range

The difference between the 75th and 25th percentiles of a data set, representing the spread of the middle 50% of the values.