Two independent samples of a random variable X are taken. Determine the expected value and variance of the sample mean estimate of uX if the PDF is exponential, (i. e. fX (x) = exp (– x) u(x)).
Answer to relevant QuestionsProve that if a sequence converges in distribution to a constant value, then it also converges in probability. This one together constitute an alternative proof to the weak law of large numbers. A communication system transmits bits over a channel such that the probability of being received in error is ρ = 0.02. Bits are transmitted in blocks of length 1023 bits and an error correction scheme is used such that bit ...You collect a sample size N1 of data and find that a 90% confidence level has width, w. What should the sample size N2 be to increase the confidence level to 99.9% and yet maintain the same interval width, w? Suppose that Xk is a sequence of IID Gaussian random variables. Recall that the sample variance is given by (a) Show that the sample variance can be written as a quadratic form ŝ2 = XTBX and find the corresponding form of ...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, ± ...
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