(e) E[V[Z X]], E[V[ZY], E[V[ZIX, Y]]. Question 4 Let X be a normal random variable with the following probability density function (pdf): 1 1 f(x| 4, 02 ) = exp V2702 202 ( - 4)2 Consider an i.i.d. sample {Xi}=lin of X. (a) Derive the log-likelihood function, ( = In C, associated with the sample {Xi}i=1in (b) Find the maximum likelihood estimators of / and o?. Question 5 Consider a normally distributed random variable X with a population mean of . From an i.i. sample {Xi}i=lin with n = 20 we obtain the sample mean X = 0.6 and the sample variance s = Perform a hypothesis test at a 5% significance level whether the population mean of X equals