Probability and Statistics - The Science of Uncertainty, Second Edition CHAPTER 2 Solutions

I have digitized some of my solutions to this textbook chapter, I hope people find this useful.

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Probability & Statistics Ch.2 Section 1 Question 1

Finding minimum and maximum values of random variables X(s)=s² and Y(s)=1/s on the sample space S={1,2,3...}

Probability & Statistics Ch.2 Section 1 Question 2

Determining whether relations between random variables X, Y, and Z are true or false on a finite sample space

Probability & Statistics Ch.2 Section 1 Question 3

Defining nonconstant random variables and computing Z(s) = X + Y² for all elements in a sample space

Probability & Statistics Ch.2 Section 1 Question 4

Computing Z(s) = XY for rolling a fair six-sided die where X(s)=s and Y(s)=s³+2

Probability & Statistics Ch.2 Section 1 Question 5

Determining if the product of two indicator functions is itself an indicator function

Probability & Statistics Ch.2 Section 1 Question 6

Computing W = X + Y + Z for indicator functions and determining if W ≥ Z

Probability & Statistics Ch.2 Section 1 Question 7

Computing W = X - Y + Z for indicator functions and determining if W ≥ Z

Probability & Statistics Ch.2 Section 1 Question 8

Computing W = X + Y + Z for indicator functions on S={1,2,3,4,5}

Probability & Statistics Ch.2 Section 1 Question 9

Computing Y(s) = s²X(s) where X is an indicator function

Probability & Statistics Ch.2 Section 1 Question 10

Exploring whether random variables must be non-negative and when X + c ≥ 0 holds

Probability & Statistics Ch.2 Section 1 Question 11

Can an unbounded random variable be defined on a finite sample space?

Probability & Statistics Ch.2 Section 1 Question 12

Must a random variable taking only values 0 or 1 be an indicator function?

Probability & Statistics Ch.2 Section 1 Question 13

How many different indicator functions can be defined on a finite sample space of size m?

Probability & Statistics Ch.2 Section 1 Question 14

Is Y = √X a random variable if X is a random variable?

Probability & Statistics Ch.2 Section 2 Question 1

Computing P(X=x) for the number of heads when flipping two fair coins

Probability & Statistics Ch.2 Section 2 Question 2

Computing the probability function for number of heads in three coin flips

Probability & Statistics Ch.2 Section 2 Question 3

Computing the probability function for the sum of two dice

Probability & Statistics Ch.2 Section 2 Question 4

Computing probability functions for W, V, ZW, VW, and V+W from a single die roll

Probability & Statistics Ch.2 Section 2 Question 5

Computing probability functions for drawing labeled chips with replacement

Probability & Statistics Ch.2 Section 2 Question 6

Computing probability functions for card values and suits from a standard deck

Probability & Statistics Ch.2 Section 2 Question 7

Computing P(X=x) for questionnaire length based on student gender

Probability & Statistics Ch.2 Section 2 Question 8

Computing P(W=w) for W = X₁ + 10X₂ when drawing numbered chips

Probability & Statistics Ch.2 Section 3 Question 1

Finding the probability function for the sum of two dice

Probability & Statistics Ch.2 Section 3 Question 2

Finding probability functions for Z and W from a coin flip

Probability & Statistics Ch.2 Section 3 Question 3

Finding the probability function for Z = XY from two coin flips

Probability & Statistics Ch.2 Section 3 Question 4

Finding probability functions for Z = X + Y and W = XY from two coin flips

Probability & Statistics Ch.2 Section 3 Question 5

Finding the probability function for the product of two dice

Probability & Statistics Ch.2 Section 3 Question 6

Computing P(5 ≤ Z ≤ 9) for a Geometric distribution

Probability & Statistics Ch.2 Section 3 Question 7

Finding the value of θ that maximizes P(X = 11) for a Binomial distribution

Probability & Statistics Ch.2 Section 3 Question 8

Finding the value of λ that maximizes P(W = 11) for a Poisson distribution

Probability & Statistics Ch.2 Section 3 Question 9

Computing P(Z ≤ 2) for a Negative-Binomial distribution

Probability & Statistics Ch.2 Section 3 Question 10

Computing P(X² ≤ 15) for a Geometric distribution

Probability & Statistics Ch.2 Section 3 Question 11

Computing P(Y = 10) for a Binomial distribution

Probability & Statistics Ch.2 Section 3 Question 12

Finding the probability function of Y = X - 7 when X is Poisson distributed

Probability & Statistics Ch.2 Section 3 Question 13

Computing probabilities for a Hypergeometric distribution

Probability & Statistics Ch.2 Section 3 Question 14

Finding the distribution and probability for die rolls recording event {2,3,5,6}

Probability & Statistics Ch.2 Section 3 Question 15

Computing basketball shooting probabilities using Binomial, Geometric, and Negative-Binomial distributions

Probability & Statistics Ch.2 Section 3 Question 16

Computing probabilities for drawing balls with replacement using Binomial, Geometric, and Negative-Binomial distributions

Probability & Statistics Ch.2 Section 3 Question 17

Finding probability distributions for drawing balls without replacement using Hypergeometric distribution

Probability & Statistics Ch.2 Section 3 Question 18

Computing probabilities for Poisson processes in queuing theory

Probability & Statistics Ch.2 Section 3 Question 19

Using Poisson distribution to approximate binomial probability for rare events

Probability & Statistics Ch.2 Section 3 Question 20

Computing probability of loop executions using Geometric distribution

Probability & Statistics Ch.2 Section 4 Question 1

Computing probabilities for a Uniform[0,1] distribution

Probability & Statistics Ch.2 Section 4 Question 2

Computing probabilities for a Uniform[1,4] distribution

Probability & Statistics Ch.2 Section 4 Question 3

Computing probabilities for an Exponential(4) distribution

Probability & Statistics Ch.2 Section 4 Question 4

Finding constants c that make various functions valid probability densities

Probability & Statistics Ch.2 Section 4 Question 5

Determining if f(x) = x/3 for -1 < x < 2 is a valid density function

Probability & Statistics Ch.2 Section 4 Question 6

Computing probabilities for an Exponential(3) distribution