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Question: The probability that two or more of a system's 10 components fail between consecutive inspections is 0.005, while the probability that only one component fails is 0.1. When two or more components fail, a re-evaluation of the system is initiated during which all failed components, and those deemed unreliable, are replaced. Otherwise, components are replaced upon their failure. Find the probability that a system re-evaluation occurs before any component is individually replaced. (Hint. Let B = {system re-evaluation occurs}, C = {a component is individually replaced}, and consider a new experiment with reduced sample space A = B ∪ C. The desired probability is the probability of B in this new experiment. See also Example).
Example: Fair game with an unfair coin. Suppose that when a biased coin is flipped it results in heads with probability p. A fair game with such an unfair coin can be played as follows: Flip the coin twice. If the outcome is (H, H) or (T, T) ignore the outcome and flip the coin two more times. Repeat until the outcome of the two flips is either (H, T) or (T, H). Code the first of these outcomes as 1 and the second as 0. Prove that the probability of getting a 1 equals 0.5.
Identify each independent variable as quantitative or qualitative. For qualitative variables, suggest several levels that might be observed. For quantitative variables, give a range of values (levels) for which the variable might be observed.
What is the mean and standard deviation of the sampling distribution when we take all samples of size25?
Describe the chi-square distribution. What is the parameter (parameters) of such a distribution?
Samples of daily production volume for the three methods are as follows. Assume that these are random samples from the populations of daily production volume. Use the median test to help determine whether the three methods are equally effective.
suppose that the probability is .3 that any given citrus tree will show measurable damage when the temperature falls to
The lifetimes of light bulbs of a particular type are normally distributed with a mean of 370 hours and a standard deviation of 5 hours. What percentage of bulbs has lifetimes that lie within 1 standard deviation of the mean on either side?
Determine the variance of firm's profit for the month.
A Correlation matrix (correlation, coefficients and probability level under the hypothesis rho = 0) for a company's sales force (age, years of service, and current sales) is given below. Comment.
Find the sample space S for this experiment.- List the outcomes in each of the events A, B, C, and D.- List the outcomes in A ∪ B, B ∪ C, and D'.
Assume that the population proportion is .55. Compute the standard error of the proportion,(), for sample sizes of 100, 200, 500, and 1000 (to 4 decimals).
which of the following correlation coefficients represents the variables with the weakest degree of
a small pilot study is run to compare a new drug for chronic pain to one that is currently available. participants are
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