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Question: Suppose that a lottery ticket has probability p of being a winning ticket, independently of other tickets. A gambler buys 3 tickets, hoping this will triple the chance of having at least one winning ticket.
(a) What is the distribution of how many of the 3 tickets are winning tickets?
(b) Show that the probability that at least 1 of the 3 tickets is winning is 3p-3p2+p3, in two different ways: by using inclusion-exclusion, and by taking the complement of the desired event and then using the PMF of a certain named distribution.
(c) Show that the gambler's chances of having at least one winning ticket do not quite triple (compared with buying only one ticket), but that they do approximately triple if p is small.
In healthy adults, x is approximately normally distributed with mean µ = 38 and standard deviation σ = 12. What is the probability that:
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State the decision rule using the .01 significance level. Compute the value of chi-square. What is your decision regarding H0?
suppose that the amount of time between consecutive surges in an electricity network has an exponential distribution
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The average salary of senior managers in the construction industry is $180,000 per year. Suppose we would like to take a sample of senior managers at a newly established company XYZ to see whether the mean annual salary is different from that ..
Calculate the test statistics
Use poisson approximation to the binomial distribution to find the probability that among 120 calls recieved by the switchboard.
1. an article in the washington post on march 16 1993 stated that nearly 45 percent of all americans have brown eyes. a
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