Question: Prove that if a sequence converges in distribution to a
Prove 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.
Answer to relevant QuestionsProve that the sequence of sample means of IID random variables converges in the MS sense. What conditions are required on the IID random variables for this convergence to occur? A certain class of students takes a standardized test where each student’s score is modeled as a random variable with mean, μ = 85, and standard deviation, σ = 5. The school will be put on probationary status if the ...Company A manufactures computer applications boards. They are concerned with the mean time before failures (MTBF), which they regularly measure. Denote the sample MTBF as ǔM and the true MTBF as μM. Determine the number of ...Suppose is a vector of IID random variables where each element has some PDF, fX (x). Find an example PDF such that the median is a better estimate of the mean than the sample mean. A wide sense stationary, discrete random process, X [n] , has an autocorrelation function of . RXX [k] Find the expected value of Y[n] =(X [n+ m] – X [n– m]) 2, where is an arbitrary integer.
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