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Let X be an r.v. (discrete or continuous) such that 0 X 1 always holds. Let = E(X). (a)
Chapter 5, Problem 53(choose chapter or problem)
QUESTION:
Let X be an r.v. (discrete or continuous) such that 0 X 1 always holds. Let = E(X). (a) Show that Var(X) 2 1 4 . Hint: With probability 1, we have X2 X. (b) Show that there is only one possible distribution for X for which Var(X)=1/4. What is the name of this distribution.
Questions & Answers
QUESTION:
Let X be an r.v. (discrete or continuous) such that 0 X 1 always holds. Let = E(X). (a) Show that Var(X) 2 1 4 . Hint: With probability 1, we have X2 X. (b) Show that there is only one possible distribution for X for which Var(X)=1/4. What is the name of this distribution.
ANSWER:Step 1 of 4
Given:
The variable X is such that 0 X 1 always holds.
Let = E(X).