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P[N=1]
P[N=1]

... Convergence of Random Variables Let X1, X2, ... be a sequence of RVs with cdf’s F1, F2, ..., and let X be another RV with cdf F. • Xn converges to X in probability, Xn P X, if for every  > 0 P[|XnX| > ]  0 as n   • Xn converges to X in distribution, Xn D X, if lim n  Fn(x) = F(x) at all x ...
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... Conditional probability Suppose there are three cards: A red card that is red on both sides, A white card that is white on both sides, and A mixed card that is red on one side and white on the other. All the cards are placed into a hat and one is pulled at random and placed on a table. If the side ...
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... Note that for this die all outcomes are not equally likely, as they would be if the die were fair. If this die is rolled 6000 times, the number of times we get a 2 or a 3 should be about A) 1000. B) 2000. C) 3000. D) 4000. E) The answer cannot be determined since the probabilities are only approxima ...
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... cards. The cards are the numbers 2 through 10 as well as four face cards, namely, jack, queen, king, and ace. What is the probability that a five-card poker hand (a) has the ace of diamonds and the queen of spades? (b) is a straight flush? A straight is five cards that have consecutive kinds. Note t ...
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Probability

Probability is the measure of the likeliness that an event will occur. Probability is quantified as a number between 0 and 1 (where 0 indicates impossibility and 1 indicates certainty). The higher the probability of an event, the more certain we are that the event will occur. A simple example is the toss of a fair (unbiased) coin. Since the two outcomes are equally probable, the probability of ""heads"" equals the probability of ""tails"", so the probability is 1/2 (or 50%) chance of either ""heads"" or ""tails"".These concepts have been given an axiomatic mathematical formalization in probability theory (see probability axioms), which is used widely in such areas of study as mathematics, statistics, finance, gambling, science (in particular physics), artificial intelligence/machine learning, computer science, game theory, and philosophy to, for example, draw inferences about the expected frequency of events. Probability theory is also used to describe the underlying mechanics and regularities of complex systems.
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