Define an infinite sequence of random variables (X.X2, X3..) on (10, 1J. B(0, 1]. Leb) by X,(0) =(1.57 - o + 1)- Find Leb([a E [0, 1]: X,(w) → I as n - 00 ). Give your answer to four decimal places. Answer:
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![Define an infinite sequence of random variables (X1. X2, X3....) on
(10, 1]. B(0, 11, Leb) by
X,(c0) =(1.57 w" + 1)-
Find
Leb([a E (0, 1] : X,(@) -→ I as n - 00).
Give your answer to four decimal places.
Answer:](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F04009b9c-c514-4798-926d-7f8b36e48162%2F8d0eef2c-23a7-486a-a6f9-1666d79afbe8%2Fz46cjmp_processed.jpeg&w=3840&q=75)
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- A time series with a periodic component can be constructed fromxt = U1 sin(2πω0t) + U2 cos(2πω0t),where U1 and U2 are independent random variables with zero means andE(U21 ) = E(U22 ) = σ2. The constant ω0 determines the period or time ittakes the process to make one complete cycle. Show that this series is weaklystationary with autocovariance functionγ(h) = σ2 cos(2πω0hA harried passenger will be several minutes late for a scheduled 10 A.M. flight to NYC. Nevertheless, he might still make the flight, since boarding is always allowed until 10:10 A.M., and boarding is sometimes permitted up to 10:30 AM. Assuming the end time of the boarding interval is uniformly distributed over the above limits, find the probability that the passenger will make his flight, assuming he arrives at the boarding gate at 10:25.In bacterial counts with a haemacytometer, the number of bacteria per quadrat has a Poisson distribution with probability mass function f(x), where f(x) = θ x e −θ/x! and θ is to be estimated. If there are many bacteria in a quadrat, it is difficult to count them all, and so the only information recorded is that the number of bacteria exceeds a certain limit c, a large positive integer. In a random sample of n quadrats, it was.
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