Probability of Chi-squared distribution

Question

If I want to find $P(\chi^2(20)<23)$, does this mean that there are assumed to be $20$ degrees of freedom, with some cumulative range of $23$?

That is, in $R$, should one use the command pchisq$(23, 20)$ or pchisq$(23^2, 20)$?

Somewhat confused.

Answer 1

Your first command is correct.

In R pchisq() function gives the cumulative probabilities. In $P(\chi^{2}(20)<23)$, the degrees of freedom is 20 and 23 is the quantile value. R's pchisq() requires the quantile value as its first argument and degrees of freedom as the second argument. In other words, the value of $P(\chi^{2}(20)<23)$ is obtained on using the command pchisq(23,20).

> pchisq(23,20)

[1] 0.7112055