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21 Φεβ 2013 · How can I estimate the probability of a random variable from one population being greater than all other random variables from unique populations?
13 Μαρ 2018 · Let X1, X2, . . . be a sequence of independent identically distributed continuous random variables. For n ≥ 2, define Xn as a record of the sequence if Xn > max (X1, X2, . . . , Xn−1), that is, if Xn is larger than each of the values observed so far. (a)Find the probability that X2 is a record.
We'll learn several different techniques for finding the distribution of functions of random variables, including the distribution function technique, the change-of-variable technique and the moment-generating function technique.
17 Αυγ 2020 · Random variables as functions. We consider in this chapter real random variables (i.e., real-valued random variables). In the chapter on Random Vectors and Joint Distributions, we extend the notion to vector-valued random quantites.
Random variables can be defined in a more rigorous manner by using the terminology of measure theory, and in particular the concepts of sigma-algebra, measurable set and probability space introduced at the end of the lecture on probability.
The sample space could be S= fa;b;cg, and the probabilities could be p(a) = 1=2, p(b) = 1=3, p(c) = 1=6. If all elements of our sample space have equal probabilities, we call this the uniform probability
Example The mileage (in thousands of miles) that car owners get with a certain kind of tire is a random variable having the density function f(x) = ˆ 1 20e x=20 if x > 0 0 if x 0; Find the probabilities that one of these tires will last (a) at most 10;000 miles; (b) anywhere from 16;000 to 24;000 miles; (c) at least 30;000 miles. Solution:
