Exam 7: A: Random Variables and Discrete Probability Distributions

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. -The number of home insurance policy holders is an example of a discrete random variable

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. $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ X 1 1 0.4 0.1 2 0.3 0.2 -{Mobile Phones Sales Narrative} Find the marginal probability distribution of the number of Blackberries sold daily.

The portfolio expected return of two investments:

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. 0 1 2 3 ( ) 0.35 0.35 0.25 0.05 -If X and Y are independent variables,then their coefficient of correlation $\rho$ = 0.

If n = 20 and p = 0.70,then the standard deviation of the binomial distribution is

Which of the following about the binomial distribution is not a true statement?

Number of Hamsters The joint probability distribution of X and Y is shown in the accompanying table,where X denotes the number of hamsters that Quinn may have next year,and Y denotes the number of hamsters that her boyfriend,Jason,may have when she moves in with him next year. $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ X 1 1 0.4 0.1 2 0.3 0.2 -{Number of Hamsters Narrative} Calculate all possible values of the conditional probabilities,for X given Y and for Y given 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} Find the probability that exactly 1 student is a sports fan.

The number of customers arriving at a department store in a 5-minute period has a binomial distribution.

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. 0 1 2 3 ( ) 0.35 0.35 0.25 0.05 -If X and Y are two variables with $\sigma _ { x } ^ { 2 } = 3.25$ , $\sigma _ { y } ^ { 2 } = 5.8$ ,and COV(X,Y)= 14.703,then the coefficient of correlation $\rho$ = 0.78.

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. $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ X 1 1 0.4 0.1 2 0.3 0.2 -{Mobile Phones Sales Narrative} Compare V(X)+ V(Y)to V(X + Y).What is your conclusion?

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. $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ X 1 1 0.4 0.1 2 0.3 0.2 -{Mobile Phones Sales Narrative} Find the marginal probability distribution of the number of Blackberries sold daily.

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

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 variance of the portfolio composed of 60% stock 1,and 40% stock 2,if the coefficient of correlation is 0.40.

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. $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ X 1 2 3 1 0.30 0.18 0.12 2 0.15 0.09 0.06 3 0.05 0.03 0.02 -{Car Sales Narrative} Calculate E(X + Y)directly by using the probability distribution of X + Y.

Another name for the mean of a probability distribution is its expected value.

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. $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ X 1 1 0.4 0.1 2 0.3 0.2 -{Mobile Phones Sales Narrative} Compute the variance of the number of Blackberries sold daily.

Shopping Outlet A shopping outlet estimates the probability distribution of the number of stores shoppers actually enter as shown in the table below. 0 1 2 3 4 ( ) 0.05 0.35 0.25 0.20 0.15 -{Shopping Outlet Narrative} Suppose Y = 2X + 1 for each value of X.What is the probability distribution of Y?

A probability distribution for a single random variable is referred to as a(n)____________________ distribution.

If X has a binomial distribution with n = 4 and p = 0.3,find P(X = 1).