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Explain why it is not possible to define a uniform distribution function (see [[guide:C9e774ade5#def 1.3 |Definition]]) | |||
uniform distribution function (see [[guide:C9e774ade5#def 1.3 |Definition]]) | |||
on a countably infinite sample space. '' Hint'': Assume <math>m(\omega) = a</math> | on a countably infinite sample space. '' Hint'': Assume <math>m(\omega) = a</math> | ||
for all | for all <math>\omega</math>, where <math>0 \leq a \leq 1</math>. Does <math>m(\omega)</math> have all the properties | ||
<math>\omega</math>, where <math>0 \leq a \leq 1</math>. Does <math>m(\omega)</math> have all the properties | of a distribution function? | ||
of | |||
a distribution function? | |||
Latest revision as of 22:07, 12 June 2024
Explain why it is not possible to define a uniform distribution function (see Definition) on a countably infinite sample space. Hint: Assume [math]m(\omega) = a[/math] for all [math]\omega[/math], where [math]0 \leq a \leq 1[/math]. Does [math]m(\omega)[/math] have all the properties of a distribution function?