2 Bookmark this page Setup: The lifetime (in months) of a battery is modeled by a random variable X that has pdf where K In (1!\"0) fo (x) K 1 ( 3-" U) for an unknown parameter 0 E (0,1). (Here 1 (x33 U) is the indicator variable that takes value 1 when its argument is true, i.e. when 3* 0.) Assume that we have n independent observations X1...,X, of the lifetime of n batteries. We want to use these observations to estimate e e (0,1) Input instructions: For all problems below, when inputting the natural log function, use In, e.g. enter In(theta) for In (0). Expectation and Variance 2 points possible (graded, results hidden) Compute the expected value E[X] and the variance Var [X of Xi (Enter your answer in terms of 8 only.) Hint: Note that the given pdf is equivalent to the pdf of a common distribution except reparametrized with a different parameter. E [X Var [X STANDARD NOTATION You have used 0 of 3 attempts S ubmit S ave