Solution: (1)∫ The sum of the probabilities of random events is 1, that is, ∴ P (x = I) = 1, ∴ 3a+1/6+3a+/kloc-. (2) when X=-2,-1, 0, 1, 3, y = x 2-1,0,8, p (y = 0) = p (0. The distribution law of ∴Y is: Y=- 1, 0, 3, 8, and the corresponding probabilities are 1/5, 7/30, 1/5,1/30 respectively. ③P(0≤Y≤3)= 7/30+ 1 1/30 = 3/5 .

4 questions, (1)∫∫(-∞, ∞)f(x)dx= 1, ∴ a ∫ (-∞, ∞) dx/[e x+e (-x)] = and. (2)P { 0 & lt； X & lt(ln3)/2} = ∫ (0, (ln3)/2) f (x) dx = (2/π) arctan (e x) 丨 (x=0, (ln3)/2)= 1/6.

5 questions, ∫ x ~ u (2,6), ∴ f (x) =1/(6-2) =1/4,2.

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