Why does the chi squared distribution intersect the y axis at 0.5 when df=2

Question

This should be failry intuaive, but i cannot figure out why chi squared distribution incepet the y axis at 0.5 when df=2

Am I correct in saying the bigger the chi^2 the bigger the difference between the expected and observed and when chi^2 is sufficiently large we can reject the fact the expected and observed are the same.

Answer 1

Your reasoning for using a chi^2 test is correct, a bigger chi^2 value is less likely so a large enough value would lead us to reject the null.

For df=2 the chi^2 distribution is equal to an exponential distribution with a rate parameter equal to 2. Beyond this there shouldn't be any intuitive reason why the y intercept is 0.5 because the y intercept depends on the value of the pdf across the whole distribution.