The random variables X and Y have the joint probability distribution given below. X=1 X=2 Y=1 0.20 0.40 Y=2 0.10 0.30
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a. Write out and draw the marginal
b. Find the
c. Write out and draw the conditional probability distribution of X, given that Y = 2.
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- Do you tailgate the car in front of you? About 30% of all drivers will tailgate before passing, thinking they can make the car in front of them go faster. Suppose that you are driving a considerable distance on a two-lane highway and are passed by 8 vehicles. (a) Let r be the number of vehicles that tailgate before passing. Make a histogram showing the probability distribution of r for r = 0 through r = 8. Maple Generated Plot Maple Generated Plot Maple Generated Plot Maple Generated PlotUse the fact that the mean of a geometric distribution is u = b. and the variance is o 1 Let x be the number of times you play the lottery before winning the first time. A daily number lottery chooses three balls numbered 0 to 9. The probability of winning the lottery is 1000 (a) Find the mean, variance, and standard deviation. (b) How many times would you expect to have to play the lottery before winning? It costs $1 to play and winners are paid $900. Would you expect to make or lose money playing this lottery? Explain. (a) The mean is (Type an integer or a decimal.) The variance is (Type an integer or a decimal.) The standard deviation is (Round to one decimal place as needed.) (b) You can expect to play the game times before winning. Would you expect to make or lose money playing this lottery? Explain. O A. You would expect to lose money. On average you would win $900 once in every times you play. So the net gain would be $ O B. You would expect to make money. On average you would…Five males with a particular genetic disorder have one child each. The random variable x is the number of children among the five who inherit the genetic disorder. Determine whether the table describes a probability distribution. If it does, find the mean and standard deviation.x012345 P(x)0.00000.00070.01050.08530.34510.5584Question content area bottomPart 1Find the mean of the random variable x. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.A.μ=enter your response here (Round to one decimal place as needed.)B.The table is not a probability distribution.Part 2Find the standard deviation of the random variable x. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.A.σ=enter your response here (Round to one decimal place as needed.)B.The table is not a probability distribution.
- Five males with an X-linked genetic disorder have one child each. The random variable x is the number of children among the five who inherit the X-linked genetic disorder. Determine whether a probability distribution is given. If a probability distribution is given, find its mean and standard deviation. If a probability distribution is not given, identify the requirements that are not satisfied. Does the table show a probability distribution? Select all that apply. X 0 1 2 3 4 5 child(ren) (Round to one decimal place as needed.) P(x) 0.027 0.152 0.321 0.321 0.152 0.027 A. Yes, the table shows a probability distribution. B. No, the random variable x is categorical instead of numerical. C. No, not every probability is between 0 and 1 inclusive. D. No, the sum of all the probabilities is not equal to 1. E. No, the random variable x's number values are not associated with probabilities. Find the mean of the random variable x. Select the correct choice below and, if necessary, fill in the…Let T = the total time it takes Professor Sawyer to get to his classroom and be ready to begin class. Describe the shape, center, and variability of the probability distribution of T.Driver’s Education. In order to determine whether or not a driver’s education course improves the scores on a driving exam, a random sample of seven students was given the exam before and after taking the course. The results are shown below. (Let d = Score After − Score Before.) Student scores in image. Compute the test statastic, and the standard error of mean.
- O The life of light bulbs is distributed normally. The variance of the lifetime is 100 and the mean lifetime of a bulb is 520 hours. Find the probability of a bulb lasting for at most 538 hours. Round your answer to four decimal places. Answer If you would like to look up the value in a table, select the table you want to view, then either click the cell at the intersection of the row and column or use the arrow keys to find the appropriate cell in the table and select it using the Space key. ny angle. 6 1 1 hp 9 a Z 2 W S X # 3 e d C A 64 $ 4 r f V % 5 t g 6 b Normal Table - to-z Normal Table -00 to z Oll y h & 7 n O u J * 8 m O i N k ( 9 < O alt 1 • JL 0 р : ctrl { [ ? / Tables O SBA + 11 Keypad Keyboard Shortcuts Submit Answer 1 USE YOUR SMARTPHONE FOR Oct 6 } ] 2:01 - 8 8 backspace 1 enter shift (inc. mean is 1 and the standard deviation is 0. O d. mean and the standard deviation can have any value. QUESTION 2 Which of the following is a characteristic of the standard normal probability distribution? a. The mean, median, and the mode are not equal b. The distribution is not symmetrical c. The standard deviation must be 0 d. The standard deviation must be 1 Click Save and Submit to save and submit. Click Save All Answers to save all answers.B12. (Excel: Calculating means, standard deviations, covariance, and correlation) Given the probability distributions of returns for stock X and stock Y, compute: a. the expected return for each stock, and b. the variance of the return for each stock c. the covariance between the returns for stock X and stock Y d. the correlation coefficient between the returns for stock X and stock Y. Probability Stock X Stock Y 0.1 -10% 4% 0.3 0 8 0.3 6 0 0.2 10 -5 0.1 20 15
- Qu A cross-tabulation of sales transactions data is shown to the right. Use the data to complete parts a Region and b below. Book DVD Total East 56 45 101 North 48 45 93 South 67 37 104 West 105 88 193 Total 276 215 491 a. Find the marginal probabilities that a sale originated in each of the four regions and the marginal probability of each type of sale (book or DVD). The marginal probability for the eastern region is The marginal probability for the northern region is The marginal probability for the southern region is The marginal probability for the western region is The marginal probability for book sales is The marginal probability for DVD sales is (Round to three decimal places as needed.) Enter your answer in the edit fields and then click Check Answer. 1 part remaining Clear All ACheck Answe This course (SummerA-QMB3200-U03A ApplicationofQuantitativeMethodsinBusiness) is based on Evans: Business Analytics: Methods, Models, anc anything. Variance: The number of cars that pass through a toll booth in an hour follows a probability distribution with the following values: NUMBER OF CARS (X) PROBABILITY P(X) 0 0.1 1 0.3 2 0.4 3 0.2 Calculate the variance of the number of cars passing through the toll booth in an hour.See attachment for the question
