Exam 7: A: Random Variables and Discrete Probability Distributions

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 uncorrelated.

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 with V(X)= 23.48 and V(Y)= 36.52,then the standard deviation of W = X + Y is $\sigma$ _w = 7.746.

A motorcycle insurance company evaluates many numerical variables about a person before deciding on an appropriate rate for motorcycle insurance.How long a person has been a licensed rider is an example of a(n)____________________ random variable.

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 standard deviation of X.

If the probability of success p remains constant in a binomial distribution,an increase in n will increase the variance.

The probability P(X $\le$ x)is called a(n)____________________ probability.The binomial table reports these probabilities.

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 random variables,which of the following identities is false?

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(4 < X < 9).

A lab at the DeBakey Institute orders 150 rats a week for each of the 52 weeks in the year for experiments that the lab conducts.Suppose the mean cost of rats used in lab experiments turned out to be $20.00 per week.Interpret this value.

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 mean of a discrete probability distribution for X is the sum of all possible values of X,divided by the number of possible values 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 -A(n)____________________ distribution provides probabilities of combinations of two random variables.

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.

Which of the following is a continuous random variable?

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 at least 1 student is a sports fan.

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

In each trial of a binomial experiment,there are ____________________ possible outcomes.

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. -A random variable is a function or rule that assigns a number to each outcome of an experiment.

Gym Visits Let X represent the number of times a student visits a gym in a one month period.Assume that the probability distribution of X is as follows: 0 1 2 3 ( ) 0.05 0.25 0.50 0.20 -{Gym Visits Narrative} Find the mean $\mu$ and the standard deviation $\sigma$ of this distribution.

Returns on Investment An analysis of the stock market produces the following information about the returns of two stocks. Stock 1 Stok 2 Bxpseted Returns 15\% 18\% Standand Deviations 20 32 Assume that the returns are positively correlated with correlation coefficient of 0.80. -{Returns on Investment Narrative} Find the mean of the return on a portfolio consisting of an equal investment in each of the two stocks.

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 variance and standard deviation of the number of Online bankers who have profited from the use of insider information.