Exam 5: Discrete Random Variables

Find the standard deviation 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 expected value of the random variable. Round to the nearest cent unless stated otherwise. -Suppose you pay $2.00 to roll a fair die with the understanding that you will get back $4.00 for rolling a 4 or a 5, nothing otherwise. What is your expected value?

Use random-variable notation to represent the event. -Suppose that two balanced dice are rolled. Let Y denote the sum of the two numbers. Use random-variable notation to represent the event that the sum of the two numbers is at least 3 but Less than 5.

Provide an appropriate response. -Three random variables X, Y, and Z, are described below. In which of these situations would it be acceptable to use the binomial distribution? A: A bag contains 4 blue marbles and 8 red marbles. Five marbles are drawn at random with Replacement. The random variable X is the number of blue marbles drawn. B: A bag contains 4 blue marbles and 8 red marbles. Six marbles are drawn at random without Replacement. The random variable Y is the number of blue marbles drawn. C: A bag contains 30 blue marbles and 38 red marbles. Three marbles are drawn at random without Replacement. The random variable Z is the number of blue marbles drawn.

Find the indicated probability. Round to four decimal places. -In one city, the probability that a person will pass his or her driving test on the first attempt is 0.63 11 people are selected at random from among those taking their driving test for the first time. What Is the probability that among these 11 people, the number passing the test is between 2 and 4 Inclusive?

Construct a probability histogram for the binomial random variable, X. -Two balls are drawn at random, with replacement, from a bag containing 4 red balls and 2 blue balls. X is the number of blue balls drawn.

Find the mean of the binomial random variable. Round to two decimal places when necessary. -A die is rolled 4 times and the number of times that two shows on the upper face is counted. If this experiment is repeated many times, find the mean for the random variable X, the number of twos.

Find the mean of the random variable. -The random variable X is the number that shows up when a loaded die is rolled. Its probability distribution is given in the table. Round the answer to two decimal places. 1 2 3 4 5 6 (=) 0.16 0.11 0.13 0.13 0.10 0.37

Find the mean of the Poisson random variable. -Suppose X has a Poisson distribution with parameter ʎ = 0.17. Find the mean of X.

Find the expected value of the random variable. Round to the nearest cent unless stated otherwise. -Sue Anne owns a medium-sized business. Use the probability distribution below, where X describes the number of employees who call in sick on a given day. Number of Employees Sick 0 1 2 3 4 (=) 0.05 0.4 0.3 0.15 0.1 What is the expected value of the number of employees calling in sick on any given day? Round The answer to two decimal places.

Evaluate the expression. - $\left( \begin{array} { c } 32 \\1\end{array} \right)$

Evaluate the expression. -(22 - 12)!

Find the specified probability. -Use the special addition rule and the following probability distribution to determine P(X = 6). 5 6 7 8 9 10 11 (=) 0.05 0.05 0.20 0.15 0.15 0.10 0.30

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. Suppose a player plays the game five times and calculates his average winnings. Will the average definitely be equal to -$0.32? Now suppose the player plays the game 100 times and calculates his average winnings. Will the average definitely be equal to -$0.32? Which average is likely to be closer to -$0.32? Explain your answer with reference to the law of large numbers.

A group of potential jurors consists of 15 women and 18 men. Suppose that 12 people are picked at random from this group, without replacement. Let X represent the number of women among those selected. Since the sample size exceeds 5% of the population size, X does not have an approximate binomial distribution. Explain in your own words why X does not have a binomial distribution. Which of the requirements for a binomial distribution does it not satisfy?

Find the standard deviation of the Poisson random variable. Round to three decimal places. -In one town, the number of burglaries in a week has a Poisson distribution with parameter $\lambda = 4.800$ . Let $\mathrm { X }$ denote the number of burglaries in the town in a randomly selected week. Find the standard deviation of X.

Find the standard deviation of the Poisson random variable. Round to three decimal places. -Suppose X has a Poisson distribution with parameter $\lambda$ = 10.620. Find the standard deviation of X.

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 exactly three living grandparents.

Find the mean of the binomial random variable. Round to two decimal places when necessary. -On a multiple choice test with 6 questions, each question has four possible answers, one of which is correct. For students who guess at all answers, find the mean for the random variable X, the Number of correct answers.

Let the random variable $X$ represent the winnings at one play of game A. The mean, $\mu$ , of $X$ is known to be $- \$ 0.42$ and its standard deviation, $\sigma$ , is $\$ 0.27$ . Let the random variable $Y$ represent the winnings at one play of game $B$ . The mean, $\mu$ , of $Y$ is known to be $- \$ 0.42$ and its standard deviation, $\sigma$ , is $\$ 0.20$ . You have decided to play one of these two games just once. At which game are you more likely to make a profit (i.e., to not lose money)? Explain your thinking.