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(a) Suppose that three random variables X1,X2, X3 form a random sample from the continuous uniform distribution on the interval [0, 1]. Assume X1, X2,X3 are independent, calculate the expectation of E[(X1 – 2X2 + X3) 2 ]. (10 marks)- (b) A particle is confined in a straight tunnel aligned in east-west direction and it can move randomly by the step size of one or two units. For each movement, the probability's p that the particle will move one unit to the west, the probability is q that the particle will move two units to the east, and the probability is 1- p - q that the particle will remain at the same place. (0 s p s 1, 0< qs 1, 0 <1-p-q< 1). A movement is independent to another. Calculate the expectation of the position of the particle after n movements, assuming that the position of starting point is 0. (10 marks)

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