Exam 7: Random Variables and Discrete Probability Distributions

The Sutton police department must write,on average,6 tickets a day to keep department revenues at budgeted levels.Suppose the number of tickets written per day follows a Poisson distribution with a mean of 6.5 tickets per day.Interpret the value of the mean.

The probability of a failure in a binomial experiment is denoted by ____________________.

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 variance of the number of Blackberries sold daily.

A(n)____________________ random variable is one whose values are countable.

Retries The following table contains the probability distribution for X = the number of retries necessary to successfully transmit a 1024K data package through a double satellite media. ​ ​ -{Retries Narrative} What is the probability of no retries?

In the notation below,X is the random variable,c is a constant,and V refers to the variance.Which of the following laws of variance is not true?

The ____________________ of a Poisson distribution is the rate at which successes occur for a given period of time or interval of space.

Number of Horses ​ The random variable X represents the number of horses per family in a rural area in Iowa,with the probability distribution: p(x)= 0.05x,x = 2,3,4,5,or 6. ​ ​ -{Number of Horses Narrative} Find the following probabilities: a.P(X ≥ 4) b.P(X > 4) c.P(3 ≤ X ≤ 5) d.P(2 < X < 4) e.P(X = 4.5)

Unsafe Levels of Radioactivity The number of incidents at a nuclear power plant has a Poisson distribution with a mean of 6 incidents per year. ​ ​ -{Unsafe Levels of Radioactivity Narrative} Find the standard deviation of the number of incidents is in one year.

In a Poisson distribution,the mean and standard deviation are equal.

Sports Fans Suppose that past history shows that 5% of college students are sports fans.A sample of 10 students is to be selected. ​ ​ -{Sports Fans Narrative} Find the probability that at most 1 student is a sports fan.

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} Find the probability distribution of X + Y.

A community college has 150 word processors.The probability that any one of them will require repair on a given day is 0.025.To find the probability that exactly 25 of the word processors will require repair,one will use what type of probability distribution?

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} Describe what happens to the standard deviation of the portfolio returns when the coefficient of correlation ρ decreases.

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} If Katie is most interested in maximizing her returns,which stock should she choose?

Golfing Store The joint probability distribution of variables X and Y is shown in the table below,where X is the number of drivers and Y is the number of putters sold daily in a small golfing store. ​ ​ -{Golfing Store Narrative} Find the probability distribution of the random variable X + Y.

Car Sales The joint probability distribution of variables X and Y is shown in the table below.Rebecca and Rachel are car salespeople.Let X denote the number of cars that Rebecca will sell in a month,and let Y denote the number of cars Rachel will sell in a month. ​ ​ -{Car Sales Narrative} Calculate E(X + Y)directly by using the probability distribution of X + Y.

Montana Highways A recent survey in Montana revealed that 60% of the vehicles traveling on highways,where speed limits are posted at 70 miles per hour,were exceeding the limit.Suppose you randomly record the speeds of ten vehicles traveling on US 131 where the speed limit is 70 miles per hour.Let X denote the number of vehicles that were exceeding the limit. ​ ​ -{Montana Highways Narrative} What is the distribution of X?

Sports Fans Suppose that past history shows that 5% of college students are sports fans.A sample of 10 students is to be selected. ​ ​ -{Sports Fans Narrative} A sample of 100 students is to be selected.What is the average number that you would expect to sports fan?

Given that X is a discrete random variable,then the laws of expected value and variance can be applied to show that E(X + 5)= E(X)+ 5,and V(X + 5)= V(X)+ 25.