# Which possible statements about the chi-squared distribution are true?a) The statistic X^2, that is

Which possible statements about the chi-squared distribution are true?
a) The statistic ${X}^{2}$, that is used to estimate the variance ${S}^{2}$ of a random sample, has a Chi-squared distribution.
b) The sum of the squares of k independent standard normal random variables has a Chi-squared distribution with k degrees of freedom.
c) The Chi-squared distribution is used in hypothesis testing and estimation.
d) The Chi-squared distribution is a particular case of the Gamma distribution.
e)All of the above.

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Raheem Donnelly
The chi-square distribution is one of the continuous probability distributions and has one parameter called degree of freedom. It is a positively skewed distribution and its domain is the set of non-negative real numbers.
The statement “The statistic, that is used to estimate the variance of a random sample, has a Chi-squared distribution” is correct as it is used in hypothesis testing for goodness of fit of the distributions to the data.
The statement “The sum of squares of independent standard normal random variables has a Chi-squared distribution with degrees of freedom” is correct as it is one of the properties of the chi-square distribution and the relationship between chi-square and standard normal distribution.
The statement “The Chi-squared distribution is used in hypothesis testing and estimation” is correct as it is used to test the goodness of fit of models, independence of attributes, equality of population variances, estimating confidence intervals for population variance and standard deviation.
The statement “The Chi-squared distribution is a particular case of the Gamma distribution” is correct as Gamma distribution with scale and shape parameters equal to 1 and 0.5 respectively reduces to Chi-square distribution with 2 degrees of freedom.
Therefore, all of the above statements are true about the Chi-squared distribution.