Difference between revisions of "Probability Norm Exercises"
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| + | |||
| + | = Exercises = | ||
<ol> | <ol> | ||
| − | <li><p> | + | <li><p>If <math>X\sim N(0,1)</math> evaluate</p> |
| + | <ol> | ||
| + | <li><p><math>\Pr (X\leq 0.2)</math></p></li> | ||
| + | <li><p><math>\Pr (X\geq 0.2)</math></p></li> | ||
| + | <li><p><math>\Pr (-0.5 \leq X \leq 1.8)</math></p></li></ol> | ||
| + | </li> | ||
| + | <li><p>Find the number <math>z_{0}</math> such that if <math>Z\sim N(0,1)</math></p> | ||
<ol> | <ol> | ||
<li><p><math>\Pr (Z\geq z_{0})=0.05</math></p></li> | <li><p><math>\Pr (Z\geq z_{0})=0.05</math></p></li> | ||
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<p>and check your answers using EXCEL.</p></li> | <p>and check your answers using EXCEL.</p></li> | ||
| − | <li><p> | + | <li><p>If <math>X\sim N(4,0.16)</math> evaluate</p> |
<ol> | <ol> | ||
<li><p><math>\Pr (X\geq 4.2)</math></p></li> | <li><p><math>\Pr (X\geq 4.2)</math></p></li> | ||
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<li><p><math>\Pr \left( (X\leq 3.8)\cup (X\geq 4.2)\right) </math></p></li></ol> | <li><p><math>\Pr \left( (X\leq 3.8)\cup (X\geq 4.2)\right) </math></p></li></ol> | ||
| − | <p>and check your answers using EXCEL. (Note for part (c), define the “events” <math>A=\left( X\leq 3.8\right) </math> and <math>B=\left( X\geq 4.2\right) </math> and calculate <math>\Pr \left( A\cup B\right)</math>.</p></li> | + | <p>and check your answers using EXCEL. (Note for part (c), define the “events” <math>A=\left( X\leq 3.8\right) </math> and <math>B=\left( X\geq 4.2\right) </math> and calculate <math>\Pr \left( A\cup B\right)</math>.</p></li></ol> |
| − | </ol> | + | |
| + | = Footnotes = | ||
Revision as of 15:27, 4 September 2014
Exercises
If [math]X\sim N(0,1)[/math] evaluate
[math]\Pr (X\leq 0.2)[/math]
[math]\Pr (X\geq 0.2)[/math]
[math]\Pr (-0.5 \leq X \leq 1.8)[/math]
Find the number [math]z_{0}[/math] such that if [math]Z\sim N(0,1)[/math]
[math]\Pr (Z\geq z_{0})=0.05[/math]
[math]\Pr (Z\lt -z_{0})=0.025[/math]
[math]\Pr (-z_{0}\lt Z\leq z_{0})=0.95[/math]
and check your answers using EXCEL.
If [math]X\sim N(4,0.16)[/math] evaluate
[math]\Pr (X\geq 4.2)[/math]
[math]\Pr (3.9\lt X\leq 4.3)[/math]
[math]\Pr \left( (X\leq 3.8)\cup (X\geq 4.2)\right) [/math]
and check your answers using EXCEL. (Note for part (c), define the “events” [math]A=\left( X\leq 3.8\right) [/math] and [math]B=\left( X\geq 4.2\right) [/math] and calculate [math]\Pr \left( A\cup B\right)[/math].
