Exam 7: A: Random Variables and Discrete Probability Distributions

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} What did you notice about the mean,variance,and standard deviation of Y = 2X + 1 in terms of the mean,variance,and standard deviation of X?

An auto insurance company evaluates many numerical variables about a person before deciding on an appropriate rate for automobile insurance.A person's age is an example of a(n)____________________ random variable.

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. 0 1 2 ( ) 0.5 0.3 0.2 y 0 1 2 ( ) 0.4 0.5 0.1 -{Number of Birds Narrative} Calculate E(X + Y)directly by using the probability distribution of X + Y.

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. 0 1 2 ( ) 0.5 0.3 0.2 y 0 1 2 ( ) 0.4 0.5 0.1 -{Number of Birds Narrative} Assume that X and Y are independent and find their bivariate distribution.

The variance of a binomial distribution for which n = 50 and p = 0.20 is 8.0.

The number of female customers out of a random sample of 100 customers arriving at a department store has a binomial distribution.

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 standard deviation of the number of sports fans you expect?

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. 0 1 2 ( ) 0.5 0.3 0.2 y 0 1 2 ( ) 0.4 0.5 0.1 -{Number of Birds Narrative} Find the probability distribution of the random variable XY.

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,then the coefficient of correlation equals ____________________.

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.

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} Calculate V(X + Y)directly by using the probability distribution of X + Y.

The ____________________ and the ____________________ both measure the relationship between two random variables X and Y.

In a bivariate distribution,the sum of all the ____________________ probabilities must equal 1.

If X is a binomial random variable with n = 25,and p = 0.25,then P(X = 25)= 1.0.

Number of Motorcycles The probability distribution of a discrete random variable X is shown below,where X represents the number of motorcycles owned by a family. 0 1 2 3 ( ) 0.25 0.40 0.20 0.15 -{Number of Motorcycles Narrative} Find the expected value of X.

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 -The ____________________ of X and Y is one measure of the strength and direction of the linear relationship between X and Y.However this number is hard to put into perspective.

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 variance and standard deviation of X.

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 perfectly positively correlated.

A binomial experiment consists of a(n)____________________ number of trials,n.

Online Bankers An official from the securities commission estimates that 75% of all online bankers have profited from the use of insider information.Assume that 15 online bankers are selected at random from the commission's registry. -{Online Bankers Narrative} Find the probability that all 15 have profited from insider information.