Suppose we form a sample variance
from a sequence of IID Gaussian random variables and then form another sample variance
from a different sequence of IID Gaussian random variables that are independent from the first set. We wish to determine if the true variances of the two sets of Gaussian random variables are the same or if they are significantly different, so we form the ratio of the sample variances
to see if this quantity is either large or small compared to 1. Assuming that the and the Yk are both standard normal, find the PDF of the statistic and show that it follows an F F distribution ( see Appendix D, Section D. 1.7).
Answer to relevant QuestionsSuppose the variance of an IID sequence of random variables is formed according to Where ů is the sample mean. Find the expected value of this estimate and show that it is biased. A discrete random process, X[n], is generated by repeated tosses of a coin. Let the occurrence of a head be denoted by 1 and that of a tail by - 1. A new discrete random process is generated by Y [2n] = X [n] for n = 0, ± ...Let s (t) be a periodic square wave as illustrated in the accompanying figure. Suppose a random process is created according to X (t) = s (t – T), where T is a random variable uniformly distributed over (0, 1). (a) Find ...Which of the following could be the correlation function of a stationary random process? (a) (b) (c) (d) (e) (f) Consider a Poisson counting process with arrival rate λ. (a) Suppose it is observed that there is exactly one arrival in the time interval [0, to]. Find the PDF of that arrival time. (b) Now suppose there were exactly two ...
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