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For the binomial lattice model, Sn = S0 Y1 × · · ·×Yn , suppose p = 0.75,d = 0.90, u = 1.5:
(a) If S0 = 2, compute E(S2 ) and V ar(S2 ).(b) If S0 = 2, compute P (S3 ≤ 2).(c) When r = 0.05: Show that the stochastic process Mn = Sn /(1 + r)n , n ≥ 0, forms a SUBmartingale
An elevator starts at the basement with 8 people (not including the elevator operator) and discharges them all by the time it reaches the top floor, number 6.
An olympic archer is able to hit the bull's-eye 70% of the time. Assume each shot is independent of the others. If she shoots 6 arrows, what is the probablitly that she never misses?
Determine what analysis would you do on each problem (i.e., one-sample z-test, one-sample t-test, proportion test, two-sample independent t-test, or paired test)?
Also explain which of the three measures of central tendency would be appropriate for your example, which would be inappropriate, and why.
Assume that you want to use a 0.05 significance level to test the claim that paired sample data come from a population for which the mean difference is Ud = 0. Find (a) d-, (b) Sd, (c) the t test statistic, and the critical values.
Describe the sampling distribution model of this mean.
Create a set of n observations from the binomial distribution with 1 trial and the event probability of 0.007, where n is your answer.
A clinical investigator is interested in understanding the relationship between demographic factors and congestive heart failure, measured by a cardiac index (CI).
Do you reject or fail to reject the null hypothesis? What is the effect size? assuming a=0.05, state your hypothesis for a one tailed test, the critical test statistic, your conclusion?
There are two rejected units. If a customer orders 180 units, what is the probability that the delivery will have at least one reject unit?
Find the indicated probability using the geometric or Poisson distribution. A newspaper finds that the mean number of typographical errors per page is nine.
Describe the shape of the distribution? what proportion of the players had no hits? how many players had 4 or fewer hits? what percentage of the players had one or fewer hits?
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