Exam 7: A: Random Variables and Discrete Probability Distributions

The binomial probability distribution is a discrete probability 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 -The sum of the expected values always equals the expected value of the sums.

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

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 ____________________,the variance of their sum is equal to the sum of their variances.

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} Find the expected mean of the portfolio.

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. -Faculty rank (professor,associate professor,assistant professor,and lecturer)is an example of a discrete random variable.

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. -For a random variable X,if V(cX)= 4V(X),where V refers to the variance,then c must be 2.

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 COV(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} Compute the mean and variance of Y.

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 coefficient of correlation is 0.5.

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 E(X + Y)and V(X + Y)directly by using the probability distribution of X + 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 standard deviation of the number of retries?

For a random variable X,E(X + 2)- 5 = E(X)-3,where E refers to the expected value.

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 any random variables with E(X)= 5,E(Y)= 6,E(XY)= 21,V(X)= 9 and V(Y)= 10,then the relationship between X and Y is a:

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} Calculate the variance and standard deviation of Y directly from the probability distribution of Y.

The standard deviation of a binomial random variable X is given by the formula $\sigma$ ² = np(1 - p),where n is the number of trials,and p is the probability of success.

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?

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 variance of the sum always equals the sum of the variances.

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(X < 3).

A portfolio expected return E(R_p)of 3 stocks with the quantities w₁ = .40,w₂ = .50,w₃ = .10,E(R₁)= .10,E(R₂)= .15,and E(R₃)= .02 is equal to 0.117.