A12 Let X₁,..., Xn be identically distributed random variables, with common expectation μ. Give a short proof of the fact that the average X = ¹₁X₂ is an unbiased estimator for f. Answer to A12: n

Let random variable X be the number of users communicating with a cellular base station within a given time interval. Its PMF is :

Let X1,..., X be an independent trials process with common expected value 2 and common variance 17. What is the exact value of the expected value of the average A? What is the variance of the average An? Your formula should have n. According to the Chebyshev inequality, P(An 20.2) ≤ (your formula should have n) Using your bound from the Chebyshev inequality, how many trials are needed so that P(An 2≥ 0.2) 0.91? (see the note below here) If you get an answer like n > 123.8, round it up to the next whole number: Your response: 124

Let X1, X2, ... be a sequence of random variables with finite mean u and non-zero variance o?. Let S, = X;. Which random variable has meanequal to 0 and variance - equal to 1? Select one: S-np O a. Zn Vno Sn-H O b. Zn Vno O c. Zn Vño O d. Zn Vno