(a) E(- log X) > – log(EX) (b) E[log(1/X)] > log[1/EX] (c) E (X³) > (EX)³
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- The conditional probability of E given that F occurs is P(EF)=___________. So in rolling a die the conditional probability of the event E, getting a six, given that the event F, getting an even number, has occurred is P(EF)=___________.Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.Consider a function F (x ) = 0, if x < 0 F (x ) = 1 − e^(−x) , if x ≥ 0 Is the corresponding random variable continuous?
- Consider a random variable X with E[X] = 10, and X being positive. Estimate E[ln√X] using Jensen’s inequality.If X is a continuous random variable with X ∼ Uniform([0, 2]), what is E[X^3]?Let X be an exponential random variable with standard deviation σ. FindP(|X − E(X)| > kσ ) for k = 2, 3, 4, and compare the results to the boundsfrom Chebyshev’s inequality.
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