Assume That a Probability Distribution Is Described by the Discrete $$\mu = \frac { n + 1 } { 2 } \text { and } \sigma = \sqrt { \frac { n ^ { 2 } - 1 } { 12 } }$$

Essay

Assume that a probability distribution is described by the discrete random variable x that can assume the values 1, 2, . . . , n; and those values are equally likely. This probability has mean and standard deviation described as follows: $$\mu = \frac { n + 1 } { 2 } \text { and } \sigma = \sqrt { \frac { n ^ { 2 } - 1 } { 12 } }$$
$\text { Show that the formulas hold for the case of }n=7$