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 mean and variance of X? Show your work.
c. Write out and draw the conditional probability distribution of X, given that Y = 2.
Show your work.
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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.
- Evaluation The monthly demand for "badi and tuyo" in Pio Duran, Albay is known to have the following probability distribution. Demand 1 2 3 4 5 6 Probability 0.20 0.10 0.05 0.05 0.30 0.30 Find the mean and the variance.Solve only letter D.If the mean and variance of a binomial distribution with parameters (n,p) are 40 and 30 respectively, then find the values of parameters n. Answer:
- Which of the following does not belong to the steps in finding the variance of probability distribution in a random variable? O Square the results of the difference between mean and random variable x. O Add the mean from each value ofa random variable x. O Find the mean of the probability distribution. O Multiply the results obtained in squaring the difference between mean and random variable x by the corresponding probability.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…Example (H.W.): Find the mean and variance from the m. g. f.of binomial distribution.
- 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.Because all Victory bus passengers do not show up for their reserved seat, the Victory liner sells n = 125 tickets for a trip that holds only 120 passengers. The probability that a passenger does not show up is 0.05. Assume that the passengers behave independently a. Find the probability that Victory liner departs with empty seats b. Calculate the mean of x c. Calculate the variance of x
