Let X be uniformly distributed in the unit interval [0, 1]

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QUESTION:

Let X be uniformly distributed in the unit interval [0, 1] . Consider the random variable Y = g(X), where g(x) = { 2 1. , if x ::; 1/3, if x > 1/3. Find the expected value of Y by first deriving its PMF. Verify the result using the expected value rule.

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QUESTION:

Let X be uniformly distributed in the unit interval [0, 1] . Consider the random variable Y = g(X), where g(x) = { 2 1. , if x ::; 1/3, if x > 1/3. Find the expected value of Y by first deriving its PMF. Verify the result using the expected value rule.

ANSWER:

Step 1 of 3

Let X be uniformly distributed in the unit interval [0, 1]. Consider the random variable

 Where

                                                               

The random variable is discrete and its probability mass function is given by

                                                             

And

                                                            

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