56. Show that the ratio of two independent standard normal random variables has the t1 distribution. Apply

Question:

56. Show that the ratio of two independent standard normal random variables has the t1 distribution. Apply the method used to derive the t pdf in this section.

Hint: Split the domain of the denominator into positive and negative parts.

1x 1/22/ 31x1x2 4 S1 X2 x2n 3n1 X1 x2n 1, X3 x2n 3

E1S2 s12/p E1S2 s 121n/22 1n 13 1n 12/24 1n 12S2/s2 x2 n1 x2n x2n

/n x2n x2

.05,2

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