Two random variables X and Y are independently distributed if all of the following conditions hold, with the exception of A. if the conditional distribution of Y given X equals the marginal distribution of Y. B. E(Y) = E[E(Yvertical line Upper X)]. C. knowing the value of one of the variables provides no information about the other. D. Pr(Y = yvertical line Upper X = x) = Pr(Y = y).

Is it true that product of 3 consecutive natural numbers is always divisible by 6? justifyyour answer

What numbers are included in the set of integers? what numbers are not included?

Atextile fiber manufacturer is investigating a new drapery yarn, which the company claims has a mean thread elongation of 12 kilograms with a standard deviation of 0.5 kilograms. the company wishes to test the hypothesis upper h subscript 0 baseline colon mu equals 12 against upper h subscript 1 baseline colon mu less-than 12 using a random sample of n equals 4 specimens. calculate the p-value if the observed statistic is x overbar equals 11.8. round your final answer to five decimal places (e. g. 98.76543).