BUS STATS: CH 5 - Discrete Probability

Which of the following can be represented by a discrete random variable?

The number of defective light bulbs in a sample of five bulbs

At a local diner, 30% of the customers order the chef's special. What is the probability that exactly one of the next five customers orders the chef's special?

0.36

The sum of the probabilities of all possible X values in a discrete distribution equals what?

1

Which of the following are examples of a binomial experiment

1. Ask customers at a movie theatre if they spent $20 or more on concessions 2. Ask randomly-selected people whether they are members of Facebook

In the following scenarios, indicate those that describe a Poisson random variable.

1. The nu per of leaks in a specified stretch of a pipeline 2. # of customers who purchase concessions over the next hour at a movie theatre

A portfolio worth $100,000 has four assets: A, B, C, and D. $10,000 is invested in A, $20,000 in B, $30,000 in C, and $40,000 in D. The portfolio weight for investment C is

30,000/100,000=0.3

At a local restaurant, 20% of the customers order the chef's special. the restaurant expects 230 customers tonight. The expected number of chef's specials that will be ordered is

46

All of the following are conditions of a binomial experiment (Bernoulli process) EXCEPT:

For each trial, the probability of a 'success' equals the probability of a 'failure'

Which of the following statements is most accurate about a Poisson random variable

It counts the number of successes in a specified time or space interval

discrete probability distribution

The probability of each value x is a value between 0 and 1, or equivalently, 0≤P(X=x)≤1 The sum of the probabilities equals 1. In other words, ΣP(X=xi)=1,where the sum extends over all values x of X.

T or F: It is common to denote random variables by upper-case letters and particular values of the random variables by the corresponding lower-case letters

True

discrete random variable

a random variable that may assume either a finite number of values or an infinite sequence of values EX:x1,x2,x3 and so on

All of the following are features of a discrete uniform distribution EXCEPT:

a. the distribution is symmetric b. the probability of each value of the distribution is the same c. the distribution is bell shaped d. the distribution has a finite number of outcomes Correct Answer: C

Expected Value of a discrete random variable

calculated as E(X)=μ=ΣxiP (X=xi)

continuous random variable

characterized by uncountable values, can take on any value within an interval or collection of intervals

Generally, the higher the positive correlation between assets' returns in a portfolio, the

greater the risk in the portfolio

random variable

is a function that assigns numerical values to the outcomes of an experiment

A Poisson random variable describes the # of successes of a certain event

over a given interval of time or in space

Expected Value

the average of each possible outcome of a future event, weighted by its probability of occurring also referred to population mean; don't confuse it with probable value

variance and standard deviation of a discrete random variable

the average of the squared differences from the mean Variance Calculated as: Var(X)=σ2=Σ(xi−μ)2P(X=xi). the positive square root of the variance St.Devs Calculated as: SD(X)=σ=√σ2

Discrete Uniform Distribution

the distribution has a finite number of specified values, each value is equally likely, the distribution is symmetric