Of n1 randomly selected engineering students at arizona state university, x1 owned an apple computer, and of n2 randomly selected engineering students at virginia tech, x2 owned an apple computer. let p1 and p2 be the probability that randomly selected asu and virginia tech engineering students, respectively, own apple computers. a. show that an unbiased estimate for p1 − p2 is (x1/n1) − (x2/n2). b. what is the standard error of the point estimate in part (a)? c. how would you compute an estimate of the standard error found in part (b)? d. suppose that n1 = 200, x1 = 150, n2 = 250, and x2 = 185. use the results of part (a) to compute an estimate of p1 − p2. e. use the results in parts (b) through (d) to compute an estimate of the standard error of the estimate.

there are lots of ways.   pick's theorem tells us if the vertices are lattice points the area a is

a = b/2 + i - 1

where b is the number of boundary lattice points and i is the number of interior lattice points.

in the figure i count b=16, i=50 so

a = 8 + 50 - 1 = 57

let's try the shoelace formula.   the area is half the sum of the cross products of the sides.  

a(-2,6)   -2(2)-6(-5) = 26

b(-5,2)   -5(-3) - 2(-2) = 19

c(-2,-3) -2(-3) - (-3)(4) = 18

d(4,-3)   4(3) - (-3)(5) = 27

e(5,3)   5(3) - 3(1) = 12

f(1,3)     1(6) - 3(-2) = 12

a(-2,6)

each of the cross products is twice the area of the triangle with the associated side and one vertex the origin. so the area of abo=26/2=13.

area = (1/2) (26 + 19 +   18 + 27 + 12 + 12) = 57

that checks!

7

step-by-step explanation:

the balance is found at the link

step-by-step explanation: