The random variable X has a probability distribution with moment-generating function of the following form: 11-1F(t)=(1 5+ bexp(t))\". Use the moment-generatingfunction technique to derive the raw moments of the distribution specied in the questions below. Then use these raw moments to derive formulas for the distributional characteristics requested. Use the moment-generating technique to derive a formula for the first raw moment of the distribution. Select the resulting formula from the list below. Select one: O E(X ) = a O E(X) = ab- O E( X) = b O E(X) = ab(1 -b) O E(X) = ab O E( X) = ath 2Determine the formula for the mean, #3:, of the distribution. Select the resulting formula from the list below. Select one: 0 #m = "3'" O #9: = (152 O n\": = b O M = a O #1. = crab Determine the formula for the variance, o2, of the distribution. Select the resulting formula from the list below. Select one: 0 2 - (a-b)2 12 O oz = ab2 O oz = a-b O 02 = ab(1 - b) O O o2 = ab(1 - a)Use the moment-generating technique to derive a formula for the second raw moment of the distribution. Select the resulting formula from the list below. Select one: 0 E(X2) = ob + W ab: 0 E(X2) = :12 + b2 0 Bar?) = ab[1 b) O E(X2) = (ab)2 0 E(X2) = a2b+ azbz ab\" 0 E(X2) = ab(1 a)