A box contains 4 black balls and 6 white balls. A player randomly draws one ball and returns the ball to the box along with 2 additional balls with the same color. Then the player randomly draws another ball. Define the random variables as If the first ball is black, Y If the first ball is white, If the second ball is black, Y, If the second ball is white, a) Find E(Y,) and Var (Y,) b) Calculate P(Y, +Y, <1) c) Calculate covariance between Y, and Y, 6 3 and 1 2 A) 5 5 5 25 1 6 and 25' 5' 25 4 2 B) 1 and 25 5 4 1 C) ' 25 1 and 5 2 D) 25 5 25 3. II II

A box contains 4 black balls and 6 white balls. A player randomly draws one ball and returns the ball to the box along with 2 additional balls with the same color. Then the player randomly draws another ball. Define the random variables as If the first ball is black, Y If the first ball is white, If the second ball is black, Y, If the second ball is white, a) Find E(Y,) and Var (Y,) b) Calculate P(Y, +Y, <1) c) Calculate covariance between Y, and Y, 6 3 and 1 2 A) 5 5 5 25 1 6 and 25' 5' 25 4 2 B) 1 and 25 5 4 1 C) ' 25 1 and 5 2 D) 25 5 25 3. II II

Name: A box contains 4 black balls and 6 white balls. A player randomly dra
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Description: A box contains 4 black balls and 6 white balls. A player randomly draws one ball andreturns the ball to the box along with 2 additional balls with the same color. Then theplayer randomly draws another ball. Define the random variables asIf the first

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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Concept explainers

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.

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Question

A box contains 4 black balls and 6 white balls. A player randomly draws one ball and
returns the ball to the box along with 2 additional balls with the same color. Then the
player randomly draws another ball. Define the random variables as
If the first ball is black,
Y =
If the first ball is white,
If the second ball is black,
Y, :
If the second ball is white,
a) Find E(Y,) and Var (Y,)
b) Calculate P(Y,+Y, <1)
c) Calculate covariance between Y and Y,
6 3
and
5
1
2
A)
5' 5 25
1
and
5
4
В)
25 5
25
1
and
25 5 25
4
1
C)
1
and
5
2
D)
25 5
25
2.
3.

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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 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 gbb, then =Rgbb1. Suppose that the random variable X is defined in terms of R as follows: =X−2R−R22. The values of X are given in the table below. Outcome ggb gbb bgb bbb bbg bgg ggg gbg Value of X −2 −1 −1 −2 −1 −2 −5 −2 Calculate the values of the probability distribution function of X , i.e. the function pX . 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 pXx
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