Exam 7: Random Variables and Discrete Probability Distributions

If X and Y are random variables,the sum of all the conditional probabilities of X given a specific value of Y will always be:

If X and Y are independent variables,then COV(X,Y)> 0.

The ____________________ of X and Y is a measure of the strength and direction of the linear relationship between X and Y.It is easy to put into perspective because it is always between −1 and 1.

The mean of a binomial distribution is equal to ____________________.

If X has a binomial distribution with n = 4 and p = 0.3,find the probability that X is at least one.

For a random variable X,V(X + 3)= V(X + 6),where V refers to the variance.

Stress Consider a binomial random variable X with n = 5 and p = 0.40,where X represents the number of times in the final exam week a student with 18 credit hours may feel stressed. ​ ​ -{Stress Narrative} Find P(2 ≤ X ≤ 4).

The following information regarding a portfolio of two stocks are given: w₁ = .25,w₂ = .75,E(R₁)= .08,and E(R₂)= .15.Which of the following regarding the portfolio expected return,E(R_p),is correct?

The Poisson random variable is a:

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} Find P(3 ≤ X ≤ 6).

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)and E(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} Find the marginal probability distribution of the number of Blackberries sold daily.

Which of the following regarding the mean and variance of a portfolio of two stocks is false?

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 probability that there will be exactly 3 incidents in a year.

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 mean or expected value for the number of retries?

In the notation below,X is the random variable,E and V refer to the expected value and variance,respectively.Which of the following is false?

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} Calculate the variances of X and Y.

The variance of a binomial distribution is equal to ____________________.

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 variance for the number of retries?

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 less than 1 student is a sports fan.