# 4. If T follows a 17 distribution, find to such that (a) P(T| to) = .05.

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3 views help_outlineImage Transcriptionclose4. If T follows a 17 distribution, find to such that (a) P(T| <。) = .9 and 0 (b) P(T > to) = .05. fullscreen
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Step 1

It is given that T follows a t distribution with  degree of freedom. Here we need to find t0 such that

P(|T|<t0) = 0.9

Step 2

here we need to find t0 such that P(|T|<t0) = 0.9. This means that there exists t0 sucht that from -t0  to t0  the distribution has an area of 0.9 as shown in below diagram.

As we know the T distirbution is symmetric we know the area to the right of t0 is half of reamaining area which half of 0.1. So it is 0.05 as shown in the diagram.

Step 3

P(-t0 < T < t0  ) = 0.9

&nbs...

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