Answered: Let W be a random variable giving the…

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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Question

Let W be a random variable giving the number of tails minus the number of heads in three tosses of a coin. Assuming that a tail is four times as likely to occur, find the probability distribution of the random variable W.

Expert Solution

Step 1

From the given information, three coins are tossed.

That is, the total number of outcomes is 2³=8.

Given that a tail is four times as likely to occur.

That is, P(T)=4P(H)......(1)

From the total probability condition,

$P (T) + P (H) = 1 4 P (H) + P (H) = 1 f r o m t h e e q u a t i o n (1) 5 P (H) = 1 P (H) = \frac{1}{5}$

Therefore,

$P (T) = 4 * \frac{1}{5} = \frac{4}{5}$

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