Difference between revisions of "Probability Norm Exercises"
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| + | = Exercises = | ||
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| + | Worked solutions to these exercises can be found here: [http://youtu.be/oh0VqlocRIA?hd=1 Q1], [http://youtu.be/KyZO83ELn_Q?hd=1 Q2] and [http://youtu.be/b-Omr-IqDhE?hd=1 Q3] | ||
<ol> | <ol> | ||
| − | <li><p>[L1, L2] | + | <li><p>[L1,L2] If <math>X\sim N(0,1)</math> evaluate</p> |
<ol> | <ol> | ||
| − | <li><p><math>\Pr (Z\geq z_{0})=0.05</math></p></li> | + | <li><p><math>\Pr (X\leq 0.23)</math> {Solution: 0.5910}</p></li> |
| − | <li><p><math>\Pr (Z<-z_{0})=0.025</math></p></li> | + | <li><p><math>\Pr (X\geq 0.23)</math> {0.4090}</p></li> |
| − | <li><p><math>\Pr (-z_{0}<Z\leq z_{0})=0.95</math></p></li></ol> | + | <li><p><math>\Pr (-0.5 \leq X \leq 1.84)</math> {0.6586}</p></li></ol> |
| + | </li> | ||
| + | <li><p>[L1,L2] Find the number <math>z_{0}</math> such that if <math>Z\sim N(0,1)</math></p> | ||
| + | <ol> | ||
| + | <li><p><math>\Pr (Z\geq z_{0})=0.05</math> {1.645}</p></li> | ||
| + | <li><p><math>\Pr (Z<-z_{0})=0.025</math> {1.96}</p></li> | ||
| + | <li><p><math>\Pr (-z_{0}<Z\leq z_{0})=0.95</math> {1.96}</p></li></ol> | ||
<p>and check your answers using EXCEL.</p></li> | <p>and check your answers using EXCEL.</p></li> | ||
<li><p>[L1,L2] If <math>X\sim N(4,0.16)</math> evaluate</p> | <li><p>[L1,L2] 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> {0.3085}</p></li> |
| − | <li><p><math>\Pr (3.9<X\leq 4.3)</math></p></li> | + | <li><p><math>\Pr (3.9<X\leq 4.3)</math> {0.3721}</p></li> |
| − | <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> {0.6170}</p></li></ol> |
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| + | <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> | ||
| − | + | = Footnotes = | |
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Latest revision as of 13:07, 5 September 2014
Exercises
Worked solutions to these exercises can be found here: Q1, Q2 and Q3
[L1,L2] If [math]X\sim N(0,1)[/math] evaluate
[math]\Pr (X\leq 0.23)[/math] {Solution: 0.5910}
[math]\Pr (X\geq 0.23)[/math] {0.4090}
[math]\Pr (-0.5 \leq X \leq 1.84)[/math] {0.6586}
[L1,L2] 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] {1.645}
[math]\Pr (Z\lt -z_{0})=0.025[/math] {1.96}
[math]\Pr (-z_{0}\lt Z\leq z_{0})=0.95[/math] {1.96}
and check your answers using EXCEL.
[L1,L2] If [math]X\sim N(4,0.16)[/math] evaluate
[math]\Pr (X\geq 4.2)[/math] {0.3085}
[math]\Pr (3.9\lt X\leq 4.3)[/math] {0.3721}
[math]\Pr \left( (X\leq 3.8)\cup (X\geq 4.2)\right)[/math] {0.6170}
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].
