Question

Find the mode of a chi square variate with 8 degrees of freedom​

Answer 1

Answer:

In probability theory and statistics, the chi-square distribution (also chi-squared or χ2-distribution) with k degrees of freedom is the distribution of a sum of the squares of k independent standard normal random variables. The chi-square distribution is a special case of the gamma distribution and is one of the most widely used probability distributions in inferential statistics, notably in hypothesis testing and in construction of confidence intervals.

 This distribution is sometimes called the central chi-square distribution, a special case of the more general noncentral chi-square distribution.

Answer 2

Concept:

The sum of the squares of k independent standard normal random variables is the chi-squared distribution with k degrees of freedom. The chi-squared distribution is a variant of the gamma distribution and one of the most used probability distributions in inferential statistics.

Find:

The mode of the chi-square variate.

Solution:

The mean of the chi-square variate is $8$.

The mode of the chi-square variate is

$=mean-2\\=8-2\\=6$

Hence, the mode is $6$.

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