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Ex 1.3. To go from A to B, Choi can take the bus with expected travel time A and standard deviation (std) σ, or the bike with expected travel time u and std T. He throws an unfair coin that lands with probability p on heads. When the outcome X is heads, he takes the bus, otherwise the bike. Let T be the expected traveling time. Use conditioning to show that E[T] = pλ + (1 − p)µ. Compute V[TIX]. Use Eve's law to compute V[T].

Ex 1.3. To go from A to B, Choi can take the bus with expected travel time A and standard deviation (std) σ, or the bike with expected travel time u and std T. He throws an unfair coin that lands with probability p on heads. When the outcome X is heads, he takes the bus, otherwise the bike. Let T be the expected traveling time. Use conditioning to show that E[T] = pλ + (1 − p)µ. Compute V[TIX]. Use Eve's law to compute V[T].

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Ex 1.3. To go from A to B, Choi can take the bus with expected travel time A and standard deviation (std) σ, or the bike with expected travel time u and std T. He throws an unfair coin that lands with probability p on heads. When the outcome X is heads, he takes the bus, otherwise the bike. Let T be the expected traveling time. Use conditioning to show that E[T] = pλ + (1 - p)µ. Compute V[T[X]. Use Eve's law to compute V[T].
Transcribed Image Text:Ex 1.3. To go from A to B, Choi can take the bus with expected travel time A and standard deviation (std) σ, or the bike with expected travel time u and std T. He throws an unfair coin that lands with probability p on heads. When the outcome X is heads, he takes the bus, otherwise the bike. Let T be the expected traveling time. Use conditioning to show that E[T] = pλ + (1 - p)µ. Compute V[T[X]. Use Eve's law to compute V[T].
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