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Let X be a normal rv with mean 1 and standard deviation 2. (a) Find P(aXa+2) when a=3. FA22 STA 310 Final (120 points) -

Let X be a normal rv with mean 1 and standard deviation 2.

(a) Find P(aXa+2) when a=3.

FA22 STA 310 Final (120 points) - Page 3 of 3 24 hours, Take-home

(b) Sketch the graph of the pdf of X, and indicate the region that corresponds to your answer in the previous part (either hand-written graph or R coding).

(c) Find the value of a such that P (a X 2) is the largest.

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