9. Let Y have a chi-square distribution with 15 degrees of freedom, let X have a chi-square...

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9. Let Y have a chi-square distribution with 15 degrees of freedom, let X have a chi-square distribution with 5 degrees of freedom, and let Y ¼ X + Z, where X and Z are independent random variables.

(a) Calculate P(y > 27.488).

(b) Calculate P(6.262 < y < 27.488).

(c) Find c such that P(y >

c) ¼ .05.

(d) Find c such that P(z >

c) ¼ .05.

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