A coin is weighted so that P(H) = and P(T) = . The coin is tossed 3 times yielding the following8-element probability space:S%3D (ННH, ННТ, НTН, HTT, TНН, THТ, TTH, TTT}Let X denote the number of heads that appear. (a) Find the distribution f of X. (b) Find E(X).

The coin is tossed 3 times yielding he following 8-element S = { HHH, HHT, HTH, HTT, THH, THT, TTH,…

Answered: A coin is weighted so that P(H) = and…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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A motorcycle drives from Welcome Rotonda to Fairview and back using the same course everyday. There are four stoplights on the course.Let x denote the number of red lights the motorcycle encounters going from Welcome Rotonda to Fairview and y denote the number encountered on the return trip. Data collected over a long period suggest that the joint probability distribution for (x, y) is given by 2 3 0.07 0.01 0.05 0.01 0.03 0.01 0.03 0.08 0.03 0.02 2 0.03 0.11 0.15 0.01 0.01 3 0.02 0.07 0.1 0.03 0.01 4 0.01 0.06 0.03 0.01 0.01 Find: 1. Standard deviation of Y. 2. Fill in the blanks As the number of motorcycle drivers from Welcome Rotonda to Fairview encountered by the motorcycle (increase, decrease, or be (zero, negative, or positive) covariance. The increases, the number of stoplights of its return trip tends to uncorrelated). Therefore, X and Y have a covariance was calculated to be (numerical value). *Describe the correlation whether a strong, a weak, or no. X and Y have correlation.…
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A coin is weighted so that P(H) = and P(T) = . The coin is tossed 3 times yielding the following 8-element probability space: %3D 4 S%3D (ННН, ННТ, НTH, HTT, THН, ТHТ, ТТH, TТT} Let X denote the number of heads that appear. (a) Find the distribution f of X. (b) Find E(X).