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A discrete random variable \( X \) takes the values \( -1,0,2 \) with the probabilities \( 1 / 4,1 / 2,1 / 4 \) respectively. Find \( V(X) \) and Standard Deviation. |
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Answer»
E(x) = \(\sum x_ip(x_i)\) = -1 x 1/4 + 0 + 1/2 + 2 x 1/4 = -1/4 + 2/4 = 1/4 E(x2) = \(\sum x_i^2p(x_i)\) = (-1)2 x 1/4 + 02 x 1/2 + 22 + 1/4 = 1/4 + 0 + 1 = 1 + 1/4 = 5/4 v(x) = E(x2) - [E(x)]2 = 5/4 - (1/4)2 = 5/4 - 1/16 = \(\frac{20-1}{16}\) = \(\frac{19}{16}\) Standard deviation \(\sigma=\sqrt{v(x)}=\sqrt{\frac{19}{16}}=\frac{\sqrt{19}}4\)
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