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