76. Let X, and s denote the sample mean and variance for the sample xị, ... , X, and let xp+1 and s1 denote these quantities when an additional obser- vation x,41 is added to the sample. a. Show how xp+1 can be computed from x, and Xn+1• b. Show that n 151 = (n – 1)8, + - - (xn+1 – Xn)² n+1 so that s+1 can be computed from x,+1, Xp, and s. c. Suppose that a sample of 15 strands of drapery yarn has resulted in a sample mean thread elongation of 12.58 mm and a sample standard deviation of .512 mm. A 16th strand results in an elongation value of 11.8. What are the values of the sample mean and sample standard deviation for all 16 elongation observations?

An urn contains 7 black and 18 white balls. A ball is randomly drawn from the urn. Let X = 1 if a white ball is drawn and let X = -1 if a black ball is drawn. Find the following a) mean of X b) variance of X Please provide your working and round your answers to 2 decimal places

If I was calculating the variance of this list of numbers (attached), do I need to include the "no home games" as a 0 and base the calculation on 14 entries?  Or do I just leave them out completely and base the calculation on 12 entries?

200 poodles 61 are left-paued left -pawed. a random sample of In a random sample ef 220 labradores 38 are Can we conclude that the difference in The tuo sample proportions of left pawed dogs is statistically significont for x= 0.05 ?