Chapter 2: Problem 2
Let \(f_{1 \mid 2}\left(x_{1} \mid x_{2}\right)=c_{1} x_{1} / x_{2}^{2},
0
Chapter 2: Problem 2
Let \(f_{1 \mid 2}\left(x_{1} \mid x_{2}\right)=c_{1} x_{1} / x_{2}^{2},
0
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Get started for freeLet \(X_{1}, X_{2}, X_{3}\) be iid with common pdf \(f(x)=\exp (-x), 0
If the random variables \(X_{1}\) and \(X_{2}\) have the joint pdf \(f\left(x_{1},
x_{2}\right)=2 e^{-x_{1}-x_{2}}, 0<\) \(x_{1}
Let \(X_{1}, X_{2}, X_{3}\) be iid, each with the distribution having pdf \(f(x)=e^{-x}, 0<\) \(x<\infty\), zero elsewhere. Show that $$Y_{1}=\frac{X_{1}}{X_{1}+X_{2}}, \quad Y_{2}=\frac{X_{1}+X_{2}}{X_{1}+X_{2}+X_{3}}, \quad Y_{3}=X_{1}+X_{2}+X_{3}$$ are mutually independent.
Let \(X_{1}, X_{2}, X_{3}\), and \(X_{4}\) be four independent random variables,
each with pdf \(f(x)=3(1-x)^{2}, 0
Let \(f(x)\) and \(F(x)\) denote, respectively, the pdf and the cdf of the random
variable \(X\). The conditional pdf of \(X\), given \(X>x_{0}, x_{0}\) a fixed
number, is defined by \(f\left(x \mid X>x_{0}\right)=f(x)
/\left[1-F\left(x_{0}\right)\right], x_{0}
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