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PPT ON PROBABILITY THEORY &STOCHASTIC PROCESS II B.Tech I semester (JNTUH-R15) ... pdf constant over the (a,b) interval and CDF is the ramp function. f 0 2 4 6 8 1 2

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In probability theory, the birthday problem concerns the probability that, in a set of n randomly chosen people, some pair of them will have the same birthday. By the pigeonhole principle, the probability reaches 100% when the number of people reaches 366 (since there are 365 possible birthdays, excluding February 29th).

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for all x2R) estimator of F. The corresponding empirical process is G n(x) = p n(F n(x) F(x)); x2R: Note that both F nand G nare stochastic processes2 indexed by the real line. By the strong law of large numbers, for every x2R, we can say that F n(x) a:s:!F(x): 1We will assume that all the random variables are de ned on the probability space (;AP).

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PPT ON PROBABILITY THEORY &STOCHASTIC PROCESS II B.Tech I semester (JNTUH-R15) ... pdf constant over the (a,b) interval and CDF is the ramp function. f 0 2 4 6 8 1 2

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2 STOCHASTIC PROCESSES B.3. Stochastic di erential equations and PDEs64 These are notes for a course on Stochastic Calculus, and are meant to supplement the texts Dur-rett, Probability: Theory and Examples; Karatzas-Sheve [KS], Brownian Motion and Stochastic Calculus; and ˜ksendahl, Stochastic Di erential Equations: An Introduction with ...

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Some familiarity with probability theory and stochastic processes, including a good understanding of conditional distributions and expectations, will be assumed. Previous exposure to the ﬁelds of application will be desirable, but not necessary. ————————————————————————- Lecture notes prepared ...