Question

If $df=2$, the chi-square distribution has a shape that reminds us of the exponential.

Short answer

The statement is true.

Step-by-step solution

Given information

Given in the question that, we have to find that whether the statement is true or false

Explanation

The gamma distribution with shape parameter $\frac{n}{2}$and scale parameter $1$can be written as shown below:

$f\left(x\right)=\frac{1}{2^{\frac{n}{2}}\mathrm{\Gamma }\left(\frac{n}{2}\right)}{x}^{\frac{n}{2}-1}{e}^{-\frac{x}{2}}$

The chi-square distribution with$2$ degrees of freedom can be written as a gamma distribution with the shape parameter as one and the scale parameter as one. And it is understood that this is the exponential distribution with scale parameter $2$. Therefore, the statement is true.