Suppose that the genders of the three children of a certain family are soon to be revealed. Outcomes are thus triples of "girls" (g) and "boys" (b), which we write as gbg, bbb, etc. For each outcome, let \( R \) be the random variable counting the number of girls in each outcome. For example, if the outcome is bgb, then \( R(bgb) = 1 \). Suppose that the random variable \( X \) is defined in terms of \( R \) as follows: \( X = 2R - 2R^2 - 3 \). The values of \( X \) are given in the table below.| Outcome | ggg | gbg | bgb | bbb | bbg | ggg | ggb | gbb ||---------|-----|-----|-----|-----|-----|-----|-----|-----|| Value of \( X \) | -15 | -7 | -3 | -3 | -3 | -7 | -7 | -3 |Calculate the values of the probability distribution function of \( X \), i.e. the function \( p_X \). First, fill in the first row with the values of \( X \). Then fill in the appropriate probabilities in the second row.| Value \( x \) of \( X \) | ??? | ??? | ??? ||--------------------------|-----|-----|-----|| \( p_X(x) \) | | | |The accompanying graphic appears to be a partial table meant to calculate the probability distribution of the variable \( X \). The placeholders indicated by question marks suggest that users should determine the distinct values of \( X \) and their corresponding probabilities based on the outcomes provided.

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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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Calculate the values of the probability distribution function of X, i.e. the function py. First, fill in the first row with the values of X. Then fill in the appropriate probabilities in the second row. Value x of X I Px (x)