Chapter 13.CR, Problem 52CR

To determine

a.

To find:

The probability density function by noting that $f\left(x\right)\ge 0$ and by finding $P\left(0\le X\le \infty \right)$.

The chi-square distribution is important in statistics for testing whether data comes from a specified distribution and for testing the independent of two characteristics of set a set of data. When a quantity called the degree of freedom is equal to 4, the probability density function is given by

$f\left(x\right)=\frac{x{e}^{-x/2}}{4}$ for $x$ in $\left[0,\infty \right)$

To determine

b.

To find:

The $P\left(0\le X\le 3\right)$ for the probability density function is given by $f\left(x\right)=\frac{x{e}^{-x/2}}{4}$ for $x$ in $\left[0,\infty \right)$.