exercise:254cd3aea4: 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> be a random variable with cumulative distribution function <math>F_X</math>, and let <math>Y = X + b</math>, <math>Z = aX</math>, and <math>W = aX + b</math>, where <math>a</math> and <math>b</math> are any constants. Find the...") |
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Let <math>X</math> be a random variable with cumulative distribution function | |||
<math>F_X</math>, and let <math>Y = X + b</math>, <math>Z = aX</math>, and <math>W = aX + b</math>, where <math>a</math> and <math>b</math> are any constants. Find the cumulative distribution functions <math>F_Y</math>, <math>F_Z</math>, and <math>F_W</math>. '' Hint'': The cases <math>a > 0</math>, <math>a = 0</math>, and <math>a < 0</math> require different arguments. | |||
<math>F_X</math>, and let <math>Y = X + b</math>, <math>Z = aX</math>, and <math>W = aX + b</math>, where <math>a</math> and <math>b</math> are any | |||
constants. Find the cumulative distribution functions <math>F_Y</math>, <math>F_Z</math>, and <math>F_W</math>. '' Hint'': | |||
The cases <math>a > 0</math>, <math>a = 0</math>, and <math>a < 0</math> require different arguments. | |||
Latest revision as of 02:04, 14 June 2024
Let [math]X[/math] be a random variable with cumulative distribution function [math]F_X[/math], and let [math]Y = X + b[/math], [math]Z = aX[/math], and [math]W = aX + b[/math], where [math]a[/math] and [math]b[/math] are any constants. Find the cumulative distribution functions [math]F_Y[/math], [math]F_Z[/math], and [math]F_W[/math]. Hint: The cases [math]a \gt 0[/math], [math]a = 0[/math], and [math]a \lt 0[/math] require different arguments.