Exam 7: Random Variables and Discrete Probability Distributions

Blackjack The probability distribution of a random variable X is shown below,where X represents the amount of money (in $1,000s)gained or lost in a particular game of Blackjack. ​ ​ -{Blackjack Narrative} Find the following probabilities: a.P(X ≤ 0) b.P(X > 3) c.P(0 ≤ X ≤ 4) d.P(X = 5)

In each trial of a binomial experiment,there are ____________________ possible outcomes.

To find the probability that X is at least 10,you should find the probability that X is 10 or ____________________.

Elizabeth's Portfolio ​ Elizabeth has decided to form a portfolio by putting 30% of her money into stock 1 and 70% into stock 2.She assumes that the expected returns will be 10% and 18%,respectively,and that the standard deviations will be 15% and 24%,respectively. ​ ​ -{Elizabeth's Portfolio Narrative} Compute the standard deviation of the returns on the portfolio assuming that the two stocks' returns are uncorrelated.

For a random variable X,E(X + 2)− 5 = E(X)− 3,where E refers to the expected value.

On the average,1.6 customers per minute arrive at any one of the checkout counters of Sunshine food market.What type of probability distribution can be used to find out the probability that there will be no customers arriving at a checkout counter in 10 minutes?

A statistical measure of the strength of the relationship between two random variables X and Y is referred to as the:

The expected value of the sum of two random variables X and Y is equal to the ____________________ of the expected value of X and the expected value of Y.

Mobile Phones Sales After analyzing sales data,the owner of a Mobile Phone store produced the following joint probability distribution of the number of iPhones (X)and Blackberries (Y)sold daily. ​ ​ -{Mobile Phones Sales Narrative} Compute the expected number of iPhones sold daily.

In Poisson experiment,the probability of more than one success in an interval approaches ____________________ as the interval becomes smaller.

Number of Birds Alana and Eva are sisters.Let X denote the number of birds that Alana may have in the next two years,and let Y denote the number of birds Eva may have during the same period.The marginal probability distributions of X and Y are shown below. ​ ​ -{Number of Birds Narrative} Determine the probability distribution of the random variable X + Y.

The variance of a portfolio of two investments will be equal to the sum of the variances of the two investments when the covariance between the investments is zero.

Katie's Portfolio ​ Katie is given the following information about the returns on two stocks: E(R₁)= 0.10,E(R₂)= 0.15,V(R₁)= 0.0225,and V(R₂)= 0.0441. ​ ​ -{Katie's Portfolio Narrative} Compute the expected value of the portfolio composed of 60% stock 1 and 40% stock 2.

A motorcycle insurance company evaluates many numerical variables about a person before deciding on an appropriate rate for motorcycle insurance.The number of tickets a person has received in the last 3 years is an example of a(n)____________________ random variable.

​ Post office The number of arrivals at a local post office between 3:00 and 5:00 P.M.has a Poisson distribution with a mean of 12. ​ ​ -{Post Office Narrative} Find the probability that the number of arrivals between 3:00 and 5:00 P.M.is at least 10.

Shopping Outlet A shopping outlet estimates the probability distribution of the number of stores shoppers actually enter as shown in the table below. ​ ​ -{Shopping Outlet Narrative} Suppose Y = 2X + 1 for each value of X.What is the probability distribution of Y?

Shopping Outlet A shopping outlet estimates the probability distribution of the number of stores shoppers actually enter as shown in the table below. ​ ​ -{Shopping Outlet Narrative} Find the expected value of the number of stores entered.

If X and Y are independent,then COV(X,Y)= ____________________.

One of the ways in which financial analysts lower the risk that is associated with the stock market is through diversification.

A motorcycle insurance company evaluates many numerical variables about a person before deciding on an appropriate rate for motorcycle insurance.The distance a person rides in a year is an example of a(n)____________________ random variable.