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1. Customers arrive in a certain shop according to an approximate Poisson process at a mean rate of 10 per hour. Let W denote the waiting time in minutes until the first two customers arrive.
(a) How is W distributed?
(b) What is the probability density function of W.
(c) What is the probability that the shopkeeper will have to wait less than 10 minutes for two customers to arrive.
2. Let Z ∼Exp(mean α). Derive E(Z) and Var(Z) using the MGF.
You determine the total nucleotide content of an rRNA molecule isolated from a bacterial cell. If the cytosine content of this rRNA molecule is 17%.
If the company wishes to estimate, within 2 percentage points and with 99% confidence, the percentage of employees who are interested in participating in a new stock option benefits program, how large a simple random sample will be necessary?
Three fair coins are tossed. Let E be the event of getting one head and let F be the event of getting two heads. Find P(F|E) and P(E|F).
Suppose that two players A and B take turns rolling a pair of balanced dice, and that the winner is the first player who obtains the sum of 7 on a given roll
indicate whether the data are a time series or a cross section.number of cars sold in a dealership each day in
A random sample of 40 clock batteries of this brand was selected. There is the probability of 0.95 that the sample mean lifetime will be less than t hours.What is the value of t?
In turning $5000 into $22 million, what were Scheiber's total and annual returns?
an experiment was performed to investigate the keyboard feel on a computer crisp or mushy and the size of the keys
What is the probability that sheer guesswork yields betwenn 25 to 30 correct answers for the test (assume the student has no knowledge of the problems). Be sure to justify why you can use the method you do.
A: There is sufficient evidence at the 0.02 level of significance that the drug stays in the system for more than 339 minutes.
By law of averages. Bystander suggests him to quit, on ground that his luck is cold. Who is correct? Or are both of them wrong?
Carry out the Wilcoxon rank sum test. State hypotheses and give the rank sum W for high- progress readers, its P-value, and your conclusion. Do the t and Wilcoxon tests lead you to different conclusions?
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