1. (4 marks) Check whether the mean and the variance of the following distributions exist: a a. fx(x) = -00 < x < ∞ (a is positive constant) T(a2+x2) b. fx(x) = {2x3 x 2 1 else 2. (5 mark) Let X be a uniformly distributed random variable with probability density function: -1 < x < 3 fx(x) = else Find the distribution for the random variable of Y = X2

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