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Continuous Random Variables and Probability Density Func­ tions. A continuous random variable takes a range of values, which may be ﬁnite or inﬁnite in extent. Here are a few examples of ranges: [0, 1], [0, ∞), (−∞, ∞), [a, b]. Deﬁnition: A random variable X is continuous if there is a function f(x) such that for any c ≤ d we ...

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Answer: A random variable merely takes the real value. For instance, if X is a random variable and C is a constant, then CX will also be a random variable. If X1 and X2 are 2 random variables, then X1+X2 plus X1 X2 will also be random. Further, for any constants C1 and C2, C1X1 + C2X2 will also be random.

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Example Let X 1 and X 2 be continuous random variables with joint density function f(x 1;x 2) = ˆ cx 1x 2 for 0 <x 1 <x 2 <1 0 otherwise: 1 Find c. 2 Find P( X 1 + 2 <1). 3 Find marginal probability density function of X 1 and 2. Boxiang Wang, The University of Iowa Chapter 2 STAT 4100 Fall 2018

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However, the PIT can be used to transform from 햴헇헂햿 ⁡ (0, 1) to a continuous random variable and this can be extended to discrete random variables. One could proceed via the general definition of F Y-1 given in Chapter 2, but there is a more intuitive approach through dividing up the area under the 햴헇헂햿 ⁡ (0, 1) density appropriately.

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