Exam 5: Discrete Random Variables

A person is trying to decide which of two possible mutual funds to invest his money in. Let the random variable X represent the annual return for mutual fund A and let the random variable Y represent the annual return for fund B. It is known that the mean, µ, of X is 10.3% and the standard deviation, Ϭ, of X is 4.2%. It is also known that the mean, µ, of Y is 11.3% and the standard deviation, Ϭ, of Y is 7.2%. Which fund do you think the person would prefer if he is a short-term investor? Which fund do you think he would prefer if he is a long-term investor? Explain your thinking.

Find the standard deviation of the Poisson random variable. Round to three decimal places. -The number of calls received by a car towing service in an hour has a Poisson distribution with parameter $\lambda$ = 1.860. Let X denote the number of calls received by the service in a randomly selected Hour. Find the standard deviation of X.

Find the standard deviation of the random variable. -The random variable X is the number of houses sold by a realtor in a single month at the Sendsom's Real Estate office. Its probability distribution is given in the table. Round the answer to two decimal Places. Houses Sold (x) 0 1 2 3 4 5 6 7 Probability () 0.24 0.01 0.12 0.16 0.01 0.14 0.11 0.21

Find the indicated probability. Round to four decimal places. -In a study, 35% of adults questioned reported that their health was excellent. A researcher wishes to study the health of people living close to a nuclear power plant. Among 10 adults randomly Selected from this area, only 3 reported that their health was excellent. Find the probability that When 10 adults are randomly selected, 3 or fewer are in excellent health.

Find the indicated probability. Round to four decimal places. -An airline estimates that 93% of people booked on their flights actually show up. If the airline books 73 people on a flight for which the maximum number is 71, what is the probability that the Number of people who show up will exceed the capacity of the plane?

Use the Poisson Distribution to find the indicated probability. Round to three decimal places when necessary. - $\lambda = 4 ; P ( X = 6 )$

Find the mean of the random variable. -The random variable X is the number of siblings of a student selected at random from a particular secondary school. Its probability distribution is given in the table. Round the answer to three Decimal places when necessary. 0 1 2 3 4 5 (=)

Find the mean of the binomial random variable. Round to two decimal places when necessary. -A company manufactures batteries in batches of 20 and there is a 3% rate of defects. Find the mean for the random variable X, the number of defects per batch.

The random variable X represents the number of siblings of a student selected randomly from a particular college. Use random variable notation to express the following statement in shorthand. The probability that the student has two siblings is $0.18$ .

Let the random variable X represent the winnings at one play of a particular game. The expected value of X is known to be -$0.32. this means that in the long run, the average amount lost by the player per play of the game will be 32 cents?

Find the specified probability. -A statistics professor has office hours from 9:00 am to 10:00 am each day. The number of students waiting to see the professor is a random variable, X, with the distribution shown in the table. 0 1 2 3 4 5 (=) 0.05 0.10 0.40 0.25 0.15 0.05 The professor gives each student 10 minutes. Determine the probability that a student arriving just after 9:00 am will have to wait no longer than 20 minutes to see the professor.

A game is said to be "fair" if the expected value for winnings is 0, that is, in the long run, the player can expect to win 0. Consider the following game. The game costs $1 to play and the payoffs are $5 for red, $3 for blue, $2 for yellow, and nothing for white. The following probabilities apply. What are your expected winnings? Does the game favor the player or the owner? Outcome Probability Red .02 Blue .04 Yellow .16 White .78

Use random-variable notation to represent the event. -For a randomly selected student in a particular high school, let Y denote the number of living grandparents of the student. Use random-variable notation to represent the event that the student Obtained has at least two living grandparents.

Obtain the probability distribution of the random variable. -The following table displays a frequency distribution for the number of siblings for students at one middle school. For a randomly selected student in the school, let X denote the number of siblings of The student. Obtain the probability distribution of X. Number of siblings 0 1 2 3 4 5 6 7 Frequency 192 246 123 56 20 9 5 1

Explain how you would construct a probability histogram of a discrete random variable given its probability distribution.

Use the Poisson Distribution to find the indicated probability. Round to three decimal places when necessary. -The number of lightning strikes in a year at the top of a particular mountain has a Poisson distribution with parameter $\lambda$ = 3.8. Find the probability that in a randomly selected year, the Number of lightning strikes is

Find the indicated binomial probability. Round to five decimal places when necessary. -In a certain college, 20% of the physics majors belong to ethnic minorities. If 10 students are selected at random from the physics majors, what is the probability that exactly 2 belong to an Ethnic minority?

Obtain the probability distribution of the random variable. -When a coin is tossed four times, sixteen equally likely outcomes are possible as shown below: HHHH HHHT HHTH HHTT HTHH HTHT HTTH HTTT THHH THHT THTH THTT TTHH TTHT TTTH TTTT Let $\mathrm { X }$ denote the total number of tails obtained in the four tosses. Find the probability distribution of the random variable X. Leave your probabilities in fraction form.

Determine the possible values of the random variable. -The following table displays a frequency distribution for the number of siblings for students in one middle school. For a randomly selected student in the school, let X denote the number of siblings of The student. What are the possible values of the random variable X? Number of siblings 0 1 2 3 4 5 6 7 Frequency 189 245 102 42 24 13 5 2

Use random-variable notation to represent the event. -Suppose that two balanced dice are rolled. Let X denote the sum of the two numbers. Use random-variable notation to represent the event that the sum of the two numbers is less than 4.