24The duration Y of long-distance telephone calls (in minutes) monitored by a station is a random variable with the properties thatP(Y= 3) = 0.3 and P(Y= 6) = 0.2.Otherwise, Y has a continuous density function given by= { 190,f(y) =ye-y/3y > 0,elsewhere.The discrete points at 3 and 6 are due to the fact that the length of the call is announced to the caller in three-minute intervals and the caller must pay forthree minutes even if he talks less than three minutes. Find the expected duration of a randomly selected long-distance call in minutes.min

P(Y=3) = 0.3 P(Y=6) = 0.2 For function : P = 1 - (0.3 + 0.2) = 0.5 Otherwise, Y has continues…

Answered: 24 The duration Y of long-distance…

A First Course in Probability (10th Edition)

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c) Let Y₁, Y₂,..., Yn be a random sample whose probability density function is given by f(v:B)= 684 - fa 00 0, elsewhere 200 200 200 and suppose that n = 200, y = 20, y = 100, y = 250 and $ = 0.025. i=1 i) Derive the standard error of ß, se(B) = 0.0009, using MLE approach. ii) Find an approximate 95% Confidence interval for B.
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