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## Homework Statement

f(x) = (3/4)(-x^2 + 6x - 8) for 2 < x < 4 (0 elsewhere)

A) Find F(x)

integral 2 to 4 ((3/4)(-x^2 + 6x - 8))dx

B) Use F(x) to find P(3 < X < 3.5)

integral 3 to 3.5 ((3/4)(-x^2 + 6x - 8))dx

11/32

C) Use F(x) to find P(X > 3.5)

1-( P(3 < X < 3.5)) = 21/31

D) Find E(X).

integral 2 to 4 (x*(3/4)(-x^2 + 6x - 8))dx = 3

E) Find the standard deviation of X.

integral 2 to 4 (x^2(3/4)(-x^2 + 6x - 8))dx E[x^2)-E[x] = sqrt(6.2)= 2.48