Three randomly selected households are surveyed. /the numbers of people in the households are 1, 3, and 8. assume that samples of size n =2 are randomly selected with replacement from the population of 1, 3, and 8. listed below are the nine different samples

1,1 ; 1,3 ; 1,8 ; 3,1 ; 3,3 ; 3,8 ; 8,1 ; 8,3 ; 8,8

find the variance of each of the nine samples then summarize the sampling distribution of the variances in the format of a table representing the probability distribution of the distinct variance values

s^2 probability

3.3

1

6.3

49

The question is asking to find the variance for the said samples in the problem ans use the sample data to determine each variance, and base on my further computation and further calculation, I would say that the answer would be the following:
#1. 3.3 -> 1 and 3 -> 2/9
#2. 1-> 0->3/9
#3. 6.3 - > 8 and 3-> 2/9
#4 49-> 1 and 8-> 2/9

Distributive property

Intersecting secant-tangent theorem states that if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.so to break it down: 1. pq acts as the tangent and ps as the secant with an intersection at p.sr = 21rp = 3x + 3pq = 4x + 4following to equation: tangent squared = the two segments multiplied by each otherso (4x + 4) ^ 2 = (3x + 3) • (21) simplifies to 16x^2 - 31x - 47 = 0 or (16x - 47)(x + 1) x = -1 or x = 47/162. pq acts as the tangent and ps as the secant with an intersection at p (again! )sr = 16rp = xpq = 15(15) ^ 2 = 16 • x225 = 16xx = 225/163. the interesting chords are proportional to each other so a ratio is possible to set up: ap dp 10 3 + x = = —— = pc pb 8 xcross multiple to get 10x = (3 + x)(8)x = 12