If $X\sim\chi^2_{df=6}$, what is the probability density function of $T = \frac{(X-6)}{\sqrt12}$?

The problem I'm confronted with is that the chi-squared random variable, $X$, can assume only positive values while the random variable $T$ can assume both positive and negative values.

I tried to use both the PDF technique and the CDF technique for transformations of random variables but in the end the PDF of $T$ could assume only positive values, that is my problem.

If $X\sim\chi^2_{6}$, what is the probability density function of $T = \frac{(X-6)}{\sqrt12}$?

The problem I'm confronted with is that the chi-squared random variable, $X$, can assume only positive values while the random variable $T$ can assume both positive and negative values.

I tried to use both the PDF technique and the CDF technique for transformations of random variables but in the end the PDF of $T$ could assume only positive values, that is my problem.

X is distributed (Central) Chi-square with 6 degrees of freedom, what is the probability density function of $T = \frac{(X-6)}{\sqrt12}$  ?

The problem is that the Chi-square random variable $(X)$ can assume only positive values while the random variable T can assume both positive and negative values, that's the problem I'm confronted with.

I tried to use both the PDF technique and the CDF technique for transformations of random variables but in the end the PDF of T could assume only positive values, that is my problem.

If $X\sim\chi^2_{df=6}$, what is the probability density function of $T = \frac{(X-6)}{\sqrt12}$?

The problem I'm confronted with is that the chi-squared random variable, $X$, can assume only positive values while the random variable $T$ can assume both positive and negative values.

I tried to use both the PDF technique and the CDF technique for transformations of random variables but in the end the PDF of $T$ could assume only positive values, that is my problem.

X is distributed (Central) Chi-square with 6 degrees of freedom, what is the probability density function of T= [X-6]/[sqrt(12)] ?

The problem is that the Chi-square random variable (X) can assume only positive values while the random variable T can assume both positive and negative values, that's the problem I'm confronted with.

I tried to use both the PDF technique and the CDF technique for transformations of random variables but in the end the PDF of T could assume only positive values, that is my problem.

X is distributed (Central) Chi-square with 6 degrees of freedom, what is the probability density function of $T = \frac{(X-6)}{\sqrt12}$ ?

The problem is that the Chi-square random variable $(X)$ can assume only positive values while the random variable T can assume both positive and negative values, that's the problem I'm confronted with.

I tried to use both the PDF technique and the CDF technique for transformations of random variables but in the end the PDF of T could assume only positive values, that is my problem.