Given Problem -

Let x1. X2, X" be a random sample of exponential RVs with parameter 1. Recall that the pdf of X; is the following: = ire-ix: xI :- 0 fix!) {I} elsewhere a.) Find the method of moments estimator for it. {3pm.} [1.1 Find the maximum likelihood estimator for it. Hotel o] using the data below, find the method of moments estimate for A. {3pts.] K1 = 13? 12 = 33.36 x3 = 5139!? N4 = 42.35 is = 15.24 K5 = 4.30 X7 = 5.68 X3 = 161:. IQ = $.49 in] = 14.33 d.l Using the tlata above. find the maximum likelihood estimate for 1.. i3pts.] e.] What is _the approximate distribution of the sample mean in = 1n], assuming your estimate for 1. in part d}? what is P{X e 20}? [4pts.i it] Using the data in o}, what is maximum likelihood estimator and estimate for B = 1H1? {3pm.}