Given f(x) = x2 1 x , find: a f(1) b f0 (1) c f00(1) d f(3)(1)

● Population Variance ○ If N is the number of values in a population with mean mu, and xi represents each individual in the population, the the population variance is found by: ○ σ 2 = sumN i=1 (xi − µ) 2 N ○ and the population standard deviation is the square root, σ = √ σ 2. ○ Most of the time we are working with a sample instead of a population. So the sample variance is found by: s 2 = Pn i=1 (xi − x¯) 2 n − 1 and the sample standard deviation is the square root, s = √ s 2. Where n is the number of observations (samples), xi is the value for the i th observation and x¯ is the sample mean. ○ By hand ­ find mean, square each scores, 1/(#­1)*(all sum square­ #*mean), then square root the ans = sd ○ If we change the data set by adding/subtract then the mean changes and sd and var remains the same ○ If multiplied or divided everything changes ● X means + sd ○ y=a+bx a and b are constants ○ mean(y)= a+b(mean(x)) ○ sd(y) = b(sd(x)) ○ var(y)=b^2(var(x)) ■ X mean (x) = 3 sd (x) = 0.5 ■ y= 3+2x mean(y) = 3+2(3) = 9 ○ sd(x) = 2(0.5) = 1 ● The function for the sample standard deviation in R is sd(data name$variable name) ● . ● Coefficient of Var