Let f(x) = = 2 π(1+x²) for x ≥ 0 and 0, elsewhere. (a) Show that f(x) is a probability density function (b) Show that the E[X] does not exist.

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For a and b

Let f(x) =
=
2
π(1+x²)
for x ≥ 0 and 0, elsewhere.
(a) Show that f(x) is a probability density function
(b) Show that the E[X] does not exist.
Transcribed Image Text:Let f(x) = = 2 π(1+x²) for x ≥ 0 and 0, elsewhere. (a) Show that f(x) is a probability density function (b) Show that the E[X] does not exist.
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