The chi-square distribution is the sum of standard normal distribution(s) squared. The degrees of freedom for a chi-square distribution is how many standard normal distribution(s) squared you are summing.
X∼N(μ,σ2)= Normal Distribution with mean 'μ' and standard deviation 'σ'
So Chi-Square Distribution with k degrees of freedom: X2=N1(0,1)2+N2(0,1)2+⋯+Nk(0,1)2
Chi-Square distribution hypothesis testing comes in handy for seeing whether the observed value of some experiment fit the expected values.
Oi: the ith observed data point Ei: the ith estimated data point