exercise:1fd7c39ffc: Difference between revisions
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(Created page with "<div class="d-none"><math> \newcommand{\NA}{{\rm NA}} \newcommand{\mat}[1]{{\bf#1}} \newcommand{\exref}[1]{\ref{##1}} \newcommand{\secstoprocess}{\all} \newcommand{\NA}{{\rm NA}} \newcommand{\mathds}{\mathbb}</math></div> Let <math>X</math> and <math>Y</math> be two random variables defined on the finite sample space <math>\Omega</math>. Assume that <math>X</math>, <math>Y</math>, <math>X + Y</math>, and <math>X - Y</math> all have the same distribution. Prove th...") |
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Let <math>X</math> and <math>Y</math> be two random variables defined on the finite sample space <math>\Omega</math>. Assume that <math>X</math>, <math>Y</math>, <math>X + Y</math>, and <math>X - Y</math> all have | |||
finite sample space <math>\Omega</math>. Assume that <math>X</math>, <math>Y</math>, <math>X + Y</math>, and <math>X - Y</math> all have | |||
the same distribution. Prove that <math>P(X = Y = 0) = 1</math>. | the same distribution. Prove that <math>P(X = Y = 0) = 1</math>. | ||
Latest revision as of 21:16, 14 June 2024
Let [math]X[/math] and [math]Y[/math] be two random variables defined on the finite sample space [math]\Omega[/math]. Assume that [math]X[/math], [math]Y[/math], [math]X + Y[/math], and [math]X - Y[/math] all have the same distribution. Prove that [math]P(X = Y = 0) = 1[/math].