Question: 2- Assume that a continuous rv X has pdf f(x) with f(-x) = f(x) and with variance equal to 1/4. (b) Compute the density of

2- Assume that a continuous rv X has pdf f(x)

2- Assume that a continuous rv X has pdf f(x) with f(-x) = f(x) and with variance equal to 1/4. (b) Compute the density of Y = |X| and show that for every r > 1, E(Y") > E(Y)". (c) Show that as n +00, the sequence { arctan(Y")} converges pointwise ae to an rv 2 with 2 ~ Bern(p) and p= P(Y > 1). Obtain an upper bound for p

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