Let $f ( x ) = \frac { 4 c } { \left( 1 + x ^ { 2 } \right) }$

question 43

Short Answer

Let $f ( x ) = \frac { 4 c } { \left( 1 + x ^ { 2 } \right) }$
a) For what value of $c$ is $f$ a probability density function?
b) For that value of $c$ , find $P ( - 1 < X < 1 )$ .

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Definitions:

Z-Scores

Standardized scores that indicate by how many standard deviations an element is from the mean.

Z-Score

Another term for standard score, indicating the number of standard deviations a data point is from the mean of its distribution.

Standard Deviations

A statistical measure that quantifies the amount of variation or dispersion of a set of data values.

Standard Normal Distribution

A bell-shaped probability distribution characterized by a mean of zero and a standard deviation of one, used in many areas of statistical analysis.