Question: Let X be a continuous variable with density and let Y = [3X + 1], where [ ] denotes the integer part. (i) Calculate the

Let X be a continuous variable with density f(x)= 3x2+1, 0, 2 0x 1, elsewhere,

and let Y = [3X + 1], where [ ] denotes the integer part.
(i) Calculate the distribution of the discrete random variable Y and then use Definition 4.4 to derive its expectation.
(ii) Is it true that the expected value of Y equals three times the integer part of the expectation of X plus one?

f(x)= 3x2+1, 0, 2 0x 1, elsewhere,

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