Hand in:
A) See below for statement of problem.
Sec.5.1 cont'd: B and C use just the algebra rules;
you can do them even if you don't "understand" the binomial, as long as
you accept X=S1+S2+...+Sn., p.340
B.) Let S be a random variable with this distribution:
s 1
0
prob p 1-p
Calculate the mean of S.(Check your answer against the calculation
of the mean of S on p. 340). Calculate the variance of S, using
the definition of variance (p. 336) . This is the fill-in for
the "hole" in the text p. 380 --- "Similarly [?] the definition
of the variance shows that sigma2S = p(1-p) "
Read and understand the rest of the derivation of the mean and s.d. of
the binomial, X, p. 340.
C) Write up the derivations of the mean and s.d. of the sample proportion
p-hat (p.342), from the mean and s.d. of the binomial X given on p. 340,
by using the fact that p-hat = X/n. This fills in the "apply the
rules" , top of p.342.
Postpone the rest:
p. 351ff
5.9b random numbers
5.5 proofreading, mean and s.d. Also, graph p(1-p) for 0<
p <1 to reinforce your understanding of part c.
5.12 random walk stocks (For part b, calculate the values using
the formula!)
5.22 trip marketing
5.24 binomial coefficient facts. (Not sure they're true?
Check with your computations in #5.12 for plausibility. Remember in any
binomial situation you can reverse the roles of Success and Failure.
Note b and c together give nC1 = n.
Normal approximation
5.17 alcohol study (this reasoning is that of significance tests,
coming up)
5.23 proportion of sample
5.25 variability on exam |
Read, discuss |
Optional
P) Do problem A below, where variance of Y = "c" pounds.
Postpone the rest:
5.26, 27 Waiting time to first success = "geometric" distribution.
Like the "chain" email problem.
Q) Calculate the "finite population correction" for n = 25, and N (population)
= 250 (10n, some texts' rule of thumb). And for N = 500 (20n, IPS's rule
of thumb). |