Prob and Stats questions

Question

a hybridization experiment begins with four peas having yellow pods and one pea having a green pod. two peas randomly selected with replacement. Find prob of peas with yellow pods. Find mean of sampling distribution. Is mean equal to population proportion of peas with yellow pods? Does mean of sampling distribution of proportions always equal the population proportion?

Answer 1

4 yellow

1 green

5 total peas

randomly select 2 peas. Pr(2Y) = 4/5 x 3/4 = 3/5 = 60% probability of drawing 2 yellow peas

Pr(1G&1Y) = 100%-60% = 40%

= 1/5 x 4/4 + 4/5 x 1/4 = .2+.2 = .4= 40%

those are the only two possible outcomes, either both yellow or only one yellow

mean = expected outcome = weighted average = .4(1Y) +.6(2Y) = .4Y+1.2Y = 1.6 yellow

not the simple unweighted average of 40 and 60%

or the mean proportion is 1.6/2 = 0.8 = 4/5 yellow

the mean is Not a possible outcome, but an average, similar to the average parents having 2.3 children, but no parents have 0.3 children.

on average the mean of a sample = the mean of the population