In probability theory and statistics , the chi-square distribution ( also chi-squared or distribution ) is one of the most widely used theoretical probability distributions . In probability theory and statistics , the chi-square distribution ( also chi-squared or ) with k degrees of freedom is the distribution of a sum of the squares of k independent standard normal random variables . It is one of the most widely used probability distributions in inferential statistics , e.g. in hypothesis testing or in construction of confidence intervals .