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# Independent and identically distributed random variables examples

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Jul 23, 2011 · Consider to independent and identically distributed random variables . The characteristic functions for X 1 − X 2 are and respectively. The product of these two functions is equivalent to the characteristic function of the sum of the random variables X 1 + ( − X 2). The result is . This is the same as the characteristic function for , which ...

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Combinations of Two Random Variables Example X and Y are independent, identically distributed (i.i.d.) random variables with common PDF f X (x)=e−xu( x) f Y (y)=e−yu( y) Find the PDF of Z=X/Y. Assume {, …,} are independent and identically distributed random variables, each with mean and finite variance . The sum X 1 + ⋯ + X n {\textstyle X_{1}+\cdots +X_{n}} has mean n μ {\textstyle n\mu } and variance n σ 2 {\textstyle n\sigma ^{2}} .