Exam 4: Discrete Random Variables and Probability Distributions

A random variable is a variable that takes on numerical values realized by the outcomes in the sample space generated by a random experiment.

Any discrete distribution is applicable when the events of interest occur randomly,independently of one another,and rarely.

The binomial probability distribution is used extensively in many applied business and economic problems.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING: On average,an RV sales lot sells six RVs per month.Assume the number of sales of RVs per month follows the Poisson distribution. -What is the probability that more than three RVs are sold next month?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING: A recent survey found that 40% of all air traffic controllers found their job extremely stressful.Suppose 12 air traffic controllers are selected at random. -What is the probability that exactly 5 of them consider their job extremely stressful?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING: It is known that 70% of the customers in a sporting goods store purchase a pair of running shoes.A random sample of 25 customers is selected.Assume that customers' purchases are made independently,and let X represent the number of customers who purchase running shoes.(Hint: Solve using Excel. ) -What is the probability that at least 17 customers purchase running shoes?

A coin toss experiment represents a binomial experiment only if the coin is balanced,i.e. ,P = 0.5.

The cumulative distribution function for a random variable X may be expressed as follows: F(x₀)= P(X < x₀).

If the outcomes of a discrete random variable follow a Poisson distribution,then their:

For a binomial probability distribution,the probability of success must always be greater than the probability of failure.

Three yellow and two blue pencils are in a drawer.If we randomly select two pencils from the drawer,find the probability distribution of X,the number of yellow pencils selected.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING: Consider the following probability distribution function. -What is the standard deviation of X?

Calculate Cov(X,Y).Did you expect this answer? Why?

On average,how many customers would you expect to see in each of these two lines at the grocery store?

Perfect linear dependency between two variables X and Y is indicated by a correlation of ±1.0.

If two random variables X and Y are independent,then P(y | x)= P(x)and P(x | y)= P(y).

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING: Suppose X and Y are two random variables with E(X)= 1.50,E(Y)= 0.55,E(XY)= 0.80,Var(X)= 0.25,and Var(Y)= 0.2475. -What is the value of E(2X - 3Y)?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING: A basketball player makes 80 percent of his free throws during the regular season.Consider his next eight free throws. -What is the probability that he will make between four and six (inclusive)free throws?

The conditional probability distribution of one random variable,given specified values of another,is the collection of conditional probabilities.

The Bernoulli model yields just two possible mutually exclusive and collectively exhaustive outcomes,which are labeled success and failure.