Applied Statistics and Probability for Engineers

8-4

Thus,

and the joint probability distribution of Tand Uis

Now, since V0, we must require that U0, and since On

rearranging this last equation, we have

The probability distribution of Tis found by

This is the distribution given in Theorem S8-1.

The probability distribution of the random variable Twas first published by W. S. Gosset

in a famous 1908 paper. Gosset was employed by the Guiness Brewers in Ireland. Since his

employer discouraged publication of employee research, Gosset published these results under

the pseudonym “Student.” As a result, this probability distribution is sometimes called the

Student t-distribution.



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