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

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It is given that T follows a t distribution with &nbsp;degree of freedom. Here we need to find t0 such that P(|T|&lt;t0) = 0.9

here we need to find t0 such that P(|T|&lt;t0) = 0.9. This means that there exists t0 sucht that from -t0&nbsp;&nbsp;to t0&nbsp;&nbsp;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.&nbsp;

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

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