Question

Consider a random variable X such that: ??(?) =|?| / 2? ??? ? ∈ {−2, −1,...

Consider a random variable X such that:
??(?) =|?| / 2? ??? ? ∈ {−2, −1, 1, 2},
??(?) = 0 ??? ? ∉ {−2, −1, 1, 2},
Where ? > 0 is a real parameter.
a) Find a.
b) What is the PMF of the random variable ? =?^2+1/??
Guidance: ? is a function of ? (? = ?(?)). Write P(? = ?) in terms of
P(? = ?) such that ? = ?(?). You can make use of the proof to the
law of the unconscious statistician from the tutorial class.

Math   Statistics-And-Probability   
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