Bi(3,0.5) is symmetrical (do you know why?), therefore does x follow this distribution?
Suppose we have some data:
x = 0, 1, 2, 3,
and the coressponding frequences:
frequency= 23, 90, 135, 52
and we want to see if the data fits a Bin(3,0.5) distribution.
My initial thoughts of how to do this was to use a goodness of fit test using chi-squared tables.
However the question asks for this to be done using only the CDF of the Bin(3,0.5) distribution.
Any ideas where to begin with this?
Formally, you have to do a chi-2 goodness-of-fit test.
For that you need the expected frequencies.
These need to be calculated using the PDF of Bin(3,0.5).
If you have the CDF instead, you need to subtract subsequent entries to find the PDF.
Btw, from the expected frequencies you will already be able to see whether it is going to fit or not.
Perhaps the problem does not require you to finish it with an actual chi-2 test?