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# Statistics for Business and Economics Chapter 4

Learn about discrete random variables and probability distributions in this chapter. Understand the mean and standard deviation, binomial probability distribution, and when to apply it. Also, explore the hypergeometric and Poisson distributions.

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## Questions and Answers

λ

E[(X − μ)²] = λ

0.0758

### What is the standard deviation of the Poisson distribution?

<p>√λ</p> Signup and view all the answers

### What is the purpose of the Poisson tables?

<p>To find the probabilities of different values of X</p> Signup and view all the answers

### What is the formula to calculate the probability of X?

<p>e^(-λ) (λ^X) / X!</p> Signup and view all the answers

### What is the expected return of the portfolio composed of 40% of Investment X and 60% of Investment Y?

<p>77</p> Signup and view all the answers

### What is the standard deviation of the portfolio composed of 40% of Investment X and 60% of Investment Y?

<p>133.04</p> Signup and view all the answers

### What is the relationship between the expected returns of Investments X and Y?

<p>μx &lt; μy</p> Signup and view all the answers

### What is the relationship between the standard deviations of Investments X and Y?

<p>σx &lt; σy</p> Signup and view all the answers

### What is the correlation coefficient (ρ) if there is a perfect positive linear dependency between X and Y?

<p>1</p> Signup and view all the answers

### What is the meaning of ρ = 0?

<p>There is no linear relationship between X and Y</p> Signup and view all the answers

### What does the covariance of 8250 between Investments X and Y indicate?

<p>The investments are positively correlated</p> Signup and view all the answers

### If X is the price for stock A and Y is the price for stock B, what is the market value, W, for the portfolio?

<p>W = aX + bY</p> Signup and view all the answers

### What statistical concept was reviewed in Chapter 4?

<p>All of the above</p> Signup and view all the answers

### What is the formula for the variance of W (σ²W)?

<p>σ²W = a²σ²X + b²σ²Y + 2abCov(X, Y)</p> Signup and view all the answers

### What is the meaning of ρ < 0?

<p>There is a perfect negative linear relationship between X and Y</p> Signup and view all the answers

### What is the formula for the mean value of W (μW)?

<p>μW = E[W] = E[aX + bY]</p> Signup and view all the answers

### What is a random variable?

<p>A numerical value from a random experiment</p> Signup and view all the answers

### What type of random variable can only take on a countable number of values?

<p>Discrete random variable</p> Signup and view all the answers

### In a random experiment, what does the number of times 4 comes up represent?

<p>A discrete random variable</p> Signup and view all the answers

### What is the chapter goal of interpreting the mean and standard deviation for a discrete random variable?

<p>To understand the mean and standard deviation for a discrete random variable</p> Signup and view all the answers

### What is the probability distribution used to find probabilities in an experiment where a coin is tossed 5 times?

<p>Binomial distribution</p> Signup and view all the answers

### What is the name of the distribution used to find probabilities when there are a fixed number of trials and the probability of success remains constant?

<p>Binomial distribution</p> Signup and view all the answers

### What is the mean of a Bernoulli distribution?

<p>P</p> Signup and view all the answers

### What is the formula for the number of sequences with x successes in n independent trials?

<p>n! / (x! * (n - x)!)</p> Signup and view all the answers

### What is a characteristic of a binomial probability distribution?

<p>Two mutually exclusive and collectively exhaustive categories</p> Signup and view all the answers

### What is the formula for the variance of a Bernoulli distribution?

<p>P(1 - P)</p> Signup and view all the answers

### What is a requirement for a binomial probability distribution?

<p>The probability of success is constant for each observation</p> Signup and view all the answers

### What is the formula for the probability of success in a Bernoulli distribution?

<p>P</p> Signup and view all the answers

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