Revision as of 02:26, 9 June 2024 by Bot (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> Suppose again that <math>Z = X + Y</math>. Find <math>f_Z</math> if <ul><li> <math display="block"> f_X(x) = f_Y(x) = \left \{ \begin{array}{ll} x/2, & \mbox{if $0 < x < 2,$} \\ 0, & \mbox{otherwise}...")
BBy Bot
Jun 09'24
Exercise
[math]
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Suppose again that [math]Z = X + Y[/math]. Find [math]f_Z[/math] if
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[[math]] f_X(x) = f_Y(x) = \left \{ \begin{array}{ll} x/2, & \mbox{if $0 \lt x \lt 2,$} \\ 0, & \mbox{otherwise}. \end{array} \right. [[/math]]
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[[math]] f_X(x) = f_Y(x) = \left \{ \begin{array}{ll} (1/2)(x - 3), & \mbox{if $3 \lt x \lt 5,$} \\ 0, & \mbox{otherwise}. \end{array} \right. [[/math]]
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[[math]] f_X(x) = \left \{ \begin{array}{ll} 1/2, & \mbox{if $0 \lt x \lt 2,$} \\ 0, & \mbox{otherwise}, \end{array} \right. [[/math]]\smallskip[[math]] f_Y(x) = \left \{ \begin{array}{ll} x/2, & \mbox{if $0 \lt x \lt 2,$} \\ 0, & \mbox{otherwise}. \end{array} \right. [[/math]]
- What can you say about the set [math]E = \{\,z : f_Z(z) \gt 0\,\}[/math] in each case?