A family of curves that depend on a parameter called degrees of freedom (df). The chi-square curve is an approximation to the probability histogram of the chi-square statistic for multinomial model if the expected number of outcomes in each category is large. The balance point of the curve is df, So the expected value of the corresponding random variable would equal df. The standard error of the corresponding random variable would be (2_df)_. As df grows, the shape of the chi-square curve approaches the shape of the normal curve.