Exam 7: Random Variables and Discrete Probability Distributions

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 σ_w = 7.746.

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?

If n = 10 and p = 0.60,then the mean of the binomial distribution is

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

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

If the covariance between two investments of a portfolio is zero,the variance of the portfolio will be equal to the sum of the variances of the investments.

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.

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. ​ ​ -{Number of Birds Narrative} Calculate V(X + Y)directly by using the probability distribution of X + Y.

911 Phone Calls 911 phone calls arrive at the rate of 30 per hour at the local call center. ​ ​ -{911 Phone Calls Narrative} If no calls are currently being processed,what is the probability that the desk employee can take four minutes break without being interrupted?

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

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. ​ ​ -{Car Sales Narrative} Determine the marginal 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. ​ ​ -{Golfing Store Narrative} Calculate E(XY).

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.

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.

Let X be a binomial random variable with n = 25 and p = 0.01. a.Use the binomial table to find P(X = 0),P(X = 1),and P(X = 2). b.Find the variance and standard deviation of X.

The Poisson random variable is a discrete random variable with infinitely many possible values.

911 Phone Calls 911 phone calls arrive at the rate of 30 per hour at the local call center. ​ ​ -{911 Phone Calls Narrative} Find the probability of receiving two calls in a five-minute interval of time.

Let X be a Poisson random variable with μ = 6.Use the table of Poisson probabilities to calculate: a.P(X ≤ 8) b.P(X = 8) c.P(X ≥ 5) d.P(6 ≤ X ≤ 10)

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. ​ ​ -{Number of Hamsters Narrative} Calculate E(XY).

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