Let X be the amount of time an ATM is in use during a particular 1-h period, and suppose that X has.

Let X be the amount of time an ATM is in use during a particular 1-h period, and suppose that X has the cdf F(x) = x θ for 0 < x="">< 1="" (where="" θ=""> 1). Give expressions involving the gamma function for both the mean and variance of the ith smallest amount of time Yi from a random sample of n such time periods. Let X represent a measurement error. It is natural to assume that the pdf f(x) is symmetric about 0, so that the density at a value -c is the same as the density at c (an error of a given magnitude is equally likely to be positive or negative). Consider a random sample of n measurements, where n =2k + 1, so that Yk+1 is the sample median. What can be said about E(Yk + 1)? If the X distribution is symmetric about some other value, so that value is the median of the distribution, what does this imply about E(Yk + 1)? [Hints: For the first question, symmetry implies that 1 – F(x) =P(X > x) =P(X < -x)="F(-x)." for="" the="" second="" question,="" consider="" w="X" -="" η;="" what="" is="" the="" median="" of="" the="" distribution="" of=""> Apr 08 2022 03:23 PM

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