Suppose the loop in Fig. P29.50 is (a) rotated about the y-axis; (b) rotated about the x-axis; (c) rotated about an edge parallel to the z-axis. What is the maximum induced emf in each case if A = 600 cm2 , v = 35.0 rad>s, and B = 0.320 T?
Elementary Statistics Exam 2 -‐ Chapters 4-‐6 Important Definitions: • Probability-‐ Chance of an event occurring • Probability Experiment-‐ Leads to well-‐defined results called outcomes • An Outcome-‐ is the result of a single trial of a probability experiment • A Sample Space-‐ Set of all possible outcomes of a probability experiment • An Event-‐ consists of outcomes • Classical Probability-‐ Number of desired outcomes / total number of possible outcomes • Empirical Probability-‐ Frequency of desired class / sum of all frequencies • Complement of An Event Experiment-‐ is the set of outcomes in the sample space that are not included in the outcomes of event P(E) = 1 – P(E) • Complement-‐ Opposite of what you want • Subjective Probability-‐ Based on guess and opinions -‐ i.e weather or sporting predictions • Mutually Exclusive-‐ Two events cannot occur at the same time. • Independent Events-‐ Two events A & B, that A occurs does not affect probability of B occurring P ( A & B ) = P ( A ) – P ( B ) • Random Variable-‐ variable whose values are determined by chance • The expected value or expectation is the mean of the probability distribution Binomial Distribution: The outcomes of a binomial experiment and the corresponding probabilities of these outcomes. Binomial Experiment: Is the probability experiment that satisfies • Each trial can have success or failure • There must be a fixed # of trials • The outcomes of each trial must be independent of each other • The probability of success must remain the same for each trial Notations: • P(S) – probability of success • P(F) – probability of failure • P -‐ # of success • Q -‐ # of failure • P(S) = p and P(F) = 1 – p = q • N – Number of trials • X – Number of successes Normal Distributions: • The normal distribution is Bell Shaped • The mean, median, and mode are equal • The normal distribution curve is unimodal • The shape is the same on both sides • The curve is continuous • The curve never touches the x-‐axis Things to remember: • The total under the normal distribution curve is equal to 1.00 • One standard deviation is 0.68 • Two standard deviations is .95 • Three standard deviations is .997 • The mean of the sample means will be the same as the population mean • Standard deviation of sample means is smaller than population • The standard deviation of the sample mean is the Standard Error of Mean • Correction for continuity may be used in the normal approximation to the binomial