Use the probability mass function of a uniform random variable with parameters a and b to find its mean.
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- The Poisson and Gaussian probability distributions of a random variable x assume a similar shape as x becomes “large.” True or FalseLet X be a chi-squared random variable with 17 degrees of freedom. What is the probability that X is greater than 10?Let X be the total medical expenses (in 1000s of dollars) incurred by a particular individual during a given year. Although X is a discrete random variable, suppose its distribution is quite well approximated by a continuous distribution with pdf What is the value of k? What is the expected value of total medical expenses? This individual is covered by an insurance plan that entails a $500 deductible provision (so the first $500 worth of expenses are paid by the individual). Then the plan will pay 80% of any additional expenses exceeding $500, and the maximum payment by the individual (including the deductible amount) is $2500. Let Y denote the amount of this individual's medical expenses paid by the insurance company. What is the expected value of Y?
- A technology manufacturing company has recently switched to the production of isolinear processors. They can make 400 processors every hour, however the probability that a randomly chosen processor works properly is 50%. Determine the probability that, of the 400 processors made this hour, at most 208 are working properly.The service time for a passport application in a certain government office is modelled as an exponential random variable with parameter λ = 5 per hour, independent and identically distributed for all applicants. Determine the probability that 50 applicants is accommodated within eight hours. Determine the maximum number of applicants such that the chance of accommodating all of them within eight hours is at least 95%.What is E(T) where is a T random variable with 17 degrees of freedom?
- Oxygen demand is a term biologists use to describe the oxygen needed by fish and other aquatic organisms for survival. The Environmental Protection Agency conducted a study of a wetland area. In this wetland environment, the mean oxygen demand was μ = 9.2 mg/L with 95% of the data ranging from 5.4 mg/L to 13.0 mg/L. Let x be a random variable that represents oxygen demand in this wetland environment. Assume xhas a probability distribution that is approximately normal. (a) Use the 95% data range to estimate the standard deviation for oxygen demand. (b) An oxygen demand below 8 indicates that some organisms in the wetland environment may be dying. What is the probability that the oxygen demand will fall below 8 mg/L?(Round your answer to four decimal places.) (c) A high oxygen demand can also indicate trouble. An oxygen demand above 12 may indicate an overabundance of organisms that endanger some types of plant life. What is the probability that the oxygen demand will exceed 12…Let A be a random variable corresponding to the sum of the outcomes of two independent rolls of a fair 6-sided die (numbered from 1 to 6). Determine the variance of A.Q3: Find the expectation and the variance of X, where X is binomial random variable X ~ Binomial (n, p), Var(X)?
- let X be a random variable and X-B(9,0.49) find the mean (expected value) of the random variable XA delivery truck travels from point A to point B and back using the same route each day. There are four traffic lights on the route. Let X1 denote the number of red lights the truck encounters going from A to B and X2 denote the number encountered on the return trip. Data collected over a long period suggest that the joint probability distribution for (X1, X2) is given by
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