Exam 7: A: Random Variables and Discrete Probability Distributions

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} Compute the covariance between X and Y.

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 the variance and standard deviation.

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 -{Retries Narrative} What is the mean or expected value for the number of retries?

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 at least 6 have profited from insider information.

Risky Undertaking Suppose you make a $2,000 investment in a risky undertaking.There is a 50% chance that the payoff from the investment will be $5,000,a 20% chance that you will just get your money back,and a 30% chance that you will receive nothing at all from your investment. -{Risky Undertaking Narrative} Find the expected value of the net profit from your investment of $2,000.

A remedial program evenly enrolls tradition and non-traditional students.If a random sample of 4 students is selected from the program to be interviewed about the introduction of a new on-line class,what is the probability that all 4 students selected are traditional students?

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

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 variance of the portfolio composed of 30% stock 1 and 70% stock 2,if the coefficient of correlation is 0.40.

The variance of a portfolio of two investments will be equal to the sum of the variances of the two investments plus twice the covariance between the investments.

An auto insurance company evaluates many numerical variables about a person before deciding on an appropriate rate for automobile insurance.The number of claims a person has made in the last 3 years is an example of a(n)____________________ random variable.

The binomial random variable is the number of successes that occur in a fixed period of time.

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 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.

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 -{Retries Narrative} What is the variance for the number of retries?

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} Use the laws of variance to calculate the variance and standard deviation of Y from the probability distribution of X.

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. $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ 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 -{Golfing Store Narrative} Are X and Y independent? Explain.

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 iPhones sold daily.

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} Compute the coefficient of correlation between X and Y.Did you expect this result? Why?

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. $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ 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 -{Golfing Store Narrative} Calculate the expected values of X and Y.

The amount of time that a microcomputer is used per week is an example of a(n)____________________ random variable.