Finding Mean, Variance, and Standard Deviation In Exercises 1-12, use the given probability density function over the indicated interval to find the (a) mean, (b) variance, and (c) standard deviation of the random variable. (d) Then sketch the graph of the density function and locate the mean on the graph. See Examples 1, 2, and 3. 1. f(x) = 3, [0,3] 2. f(x) = 1, [0,4] 3. f(t) = 1, [0, 6] 4. f(x) = x. [0,4] 5. f(x) = 4, [1,4] 3x2 6. f(x) = {x/2, [0, 1] 7. f(x) = 1x, [0,2] - 8. f(x) = x, [0,4] 9. f(x) = 6x(1x), [0, 1] 10. f(x) = x(4x), [0,4] 11. f(x)=4-x, [0,4] 12. f(x) = 18 9 x, [0, 9]