Chi-squared Distribution | R Tutorial (original) (raw)

If X1,X2,…,Xm are m independent random variables having the standard normal distribution, then the following quantity follows a Chi-Squared distribution with m degrees of freedom. Its mean is m, and its variance is2m.

V = X21 + X22 + ⋅⋅⋅+ X2m ~ χ2(m)

Here is a graph of the Chi-Squared distribution 7 degrees of freedom.

PIC

Problem

Find the 95th percentile of the Chi-Squared distribution with 7 degrees of freedom.

Solution

We apply the quantile function qchisq of the Chi-Squared distribution against the decimal values 0.95.

> qchisq(.95, df=7) # 7 degrees of freedom
[1] 14.067

Answer

The 95th percentile of the Chi-Squared distribution with 7 degrees of freedom is 14.067.