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Let X be uniformly distributed in the unit interval [0, 1]
Chapter , Problem 1(choose chapter or problem)
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.
Questions & Answers
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