10. Let Y have the density N(5, 36), X have the density N(4, 25), let Yand X...

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10. Let Y have the density N(5, 36), X have the density N(4, 25), let Yand X be independent random variables, and define W ¼ X Y.

(a) Calculate P(y > 10).

(b) Calculate P(10 < y < 10).

(c) Calculate P(w > 0).

(d) Find c such that P(w >

c) ¼ .95.

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