When integrating by parts with one factor as a variable and the other with a trig function, generally the variable will be set to u and the trig function set to dv

integral udv = uv - integral vdu

let's take integral x^2*sinx

u = x^2

du = 2x dx

dv = sinx

v = -cosx

this gives us -x^2(cosx) - integral -2xsinx

now we have to integral by parts again

u = -2x

du = -2 dx

dv = sinx

v = -cosx

2xcosx - integral 2cosx = 2xcosx -(1/2)sinx

answer is -x^2(cosx) - 2xcosx + (1/2)sinx + C

## Tuesday, December 29, 2015

## Tuesday, December 22, 2015

## Monday, December 14, 2015

## Saturday, December 12, 2015

Suppose x,y are as follows

x 1 1 1 2 2 2 3 3 3 1

y 8 9 10 8 9 10 8 9 10 10

This has a relatively strong negative correlation, but if you remove the data point (1,10), all you have left is a block of data with correlation coefficient of 0.

## Wednesday, December 9, 2015

This is what is all means

sum(x) = all x's added together

sum(y) = all y's added together

sum(x^2) = square each x, then sum the total

sum(y^2) = square each y, then sum the total

sum(xy) = muitiply each xy value , then sum the total

(sumx)^2 = sum of the x's then square

(sumy)^2 = sum of the y's, then square

r^2 is just taking r and squaring it

y-bar is the average of the y's, which is sum(y)/n

x-bar is the average of the x's, which is sum(x)/n

## Friday, December 4, 2015

1. state the Ho and Ha

2. find test statistic z or t, for proportions we can use z if np > 5 and n(1-p) or nq > 5

3. find critical value for z or t using the appropriate chart

4. make the decision on the test, if using p-value, if p-value > significance level then do not reject. If p-value < significance level of the test, reject.

5. state the conclusion

Type I error is when you reject Ho when you should not reject Ho

Type II error is when you do not reject Ho when you should reject Ho

The power of the test is the probability of not committing a type two error, which is basically the probability of making the correct decision of rejecting Ho.

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