Suppose X is a continuous random variable uniformly distributed on [-1,1]. Note that the pdf of...

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Suppose X is a continuous random variable uniformly distributed on [-1,1]. Note that the pdf of X is given by S1/2, if - 1<t<1, 1o. fx(t) = otherwise. Also, let Y = 0 X, where 0 is an unknown non-negative constant (so that 0 = |0|). (a) Compute E(Y²), and E(|Y|), possibly in terms of the unknown 0. (b) Find some 'c' (possibly in terms of 0) such that P{|Y| – c<0 < |Y|+ c} = 1/3. (c) Find an unbiased estimator for 0 in terms of Y. Suppose X is a continuous random variable uniformly distributed on [-1,1]. Note that the pdf of X is given by S1/2, if - 1<t<1, 1o. fx(t) = otherwise. Also, let Y = 0 X, where 0 is an unknown non-negative constant (so that 0 = |0|). (a) Compute E(Y²), and E(|Y|), possibly in terms of the unknown 0. (b) Find some 'c' (possibly in terms of 0) such that P{|Y| – c<0 < |Y|+ c} = 1/3. (c) Find an unbiased estimator for 0 in terms of Y.