Q.N. 1)Consider the random variable X with density given by f(x) = 0xe-On a) Derive the expression for E(X). b) Find the method of moment estimator for 0. x>0, 0>0 c) Find the maximum likelihood estimator for 0 based on a random sample of size n. Does this estimator differ from that found in part (b)? d) Estimate 0 based on the following data: ONLO) 0.1, 0.3, 0.5, 0.2, 0.3, 0.4, 0.4, 0.3, 0.3, 0.3 G 1.. (EBV)