Assignment:
Discussion:
Q1: In a lab experiment involving inorganic syntheses of molecular precursors to organometallic ceramics, the final step of a five-step reaction involves the formation of a metal-metal bond. The probability of such a bond forming is p = 0.20. Let X equal the number of successful reactions out of n = 25 such experiments.
a) Find the probability that X is at most 4
b) Find the probability that X is at least 5
c) Find the probability that X is equal to 6
d) Give the mean, variance, and standard deviation of X
b. lt is claimed that 15% of the ducks in a particular region have patent schistosome infection. Sup¬pose that seven ducks are selected at random. Let X equal the number of ducks that are infected.
(a) Assuming independence, how is X dis-tributed?
(b) Find (i) P(X z 2), (ii) P(X = 1), and (iii) P( X s 3).
Q2: An urn contains 7 red and 11 white balls. Draw one ball at random from the urn. Let X = 1 if a red ball is drawn, and let X = 0 if a white ball is drawn. Give the p.m.f., mean, and variance of X.
Q3: Suppose that X = 1 if a red ball is drawn and X = -1 if a white ball is drawn. Give the p.m.f., mean, and variance of X.