Probability Norm Exercises - Revision history

Rb at 13:07, 5 September 2014

2014-09-05T13:07:37Z

Rb at 12:13, 5 September 2014

2014-09-05T12:13:45Z

Rb at 12:06, 5 September 2014

2014-09-05T12:06:29Z

Rb at 12:05, 5 September 2014

2014-09-05T12:05:03Z

Rb at 15:30, 4 September 2014

2014-09-04T15:30:50Z

Rb: /* Exercises */

2014-09-04T15:28:58Z

‎Exercises

Rb at 15:28, 4 September 2014

2014-09-04T15:28:27Z

Rb at 15:27, 4 September 2014

2014-09-04T15:27:26Z

Rb at 12:08, 4 September 2014

2014-09-04T12:08:52Z

Rb at 12:07, 4 September 2014

2014-09-04T12:07:49Z

@@ Line 3: / Line 3: @@
 = Exercises =
-Worked solutions to these exercises can be found here: [http://youtu.be/oh0VqlocRIA?hd=1 Q1]
+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>
-<li><p><math>[L1,L2]</math> If <math>X\sim N(0,1)</math> evaluate</p>
+<li><p>[L1,L2] If <math>X\sim N(0,1)</math> evaluate</p>
 <ol>
 <li><p><math>\Pr (X\leq 0.23)</math> {Solution: 0.5910}</p></li>
@@ Line 12: / Line 12: @@
 <li><p><math>\Pr (-0.5 \leq X \leq 1.84)</math> {0.6586}</p></li></ol>
 </li>
-<li><p><math>L1,L2</math> Find the number <math>z_{0}</math> such that if <math>Z\sim N(0,1)</math></p>
+<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>
@@ Line 19: / Line 19: @@
 <p>and check your answers using EXCEL.</p></li>
-<li><p><math>L1,L2</math> 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>
 <li><p><math>\Pr (X\geq 4.2)</math> {0.3085}</p></li>
@@ Line 26: / Line 26: @@
 <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 =

@@ Line 2: / Line 2: @@
 = Exercises =
 <ol>
-<li><p><math>L1,L2</math> If <math>X\sim N(0,1)</math> evaluate</p>
+<li><p><math>[L1,L2]</math> If <math>X\sim N(0,1)</math> evaluate</p>
 <ol>
 <li><p><math>\Pr (X\leq 0.23)</math> {Solution: 0.5910}</p></li>
@@ Line 24: / Line 26: @@
 <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 =

@@ Line 1: / Line 1: @@
 = Exercises =
@@ Line 4: / Line 6: @@
 <li><p><math>L1,L2</math> If <math>X\sim N(0,1)</math> evaluate</p>
 <ol>
-<li><p><math>\Pr (X\leq 0.23)</math> Solution: 0.5910</p></li>
+<li><p><math>\Pr (X\leq 0.23)</math> {Solution: 0.5910}</p></li>
-<li><p><math>\Pr (X\geq 0.23)</math> 0.4090</p></li>
+<li><p><math>\Pr (X\geq 0.23)</math> {0.4090}</p></li>
-<li><p><math>\Pr (-0.5 \leq X \leq 1.84)</math> 0.6586</p></li></ol>
+<li><p><math>\Pr (-0.5 \leq X \leq 1.84)</math> {0.6586}</p></li></ol>
 </li>
 <li><p><math>L1,L2</math> 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\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<-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>
+<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>
 <li><p><math>L1,L2</math> If <math>X\sim N(4,0.16)</math> evaluate</p>
 <ol>
-<li><p><math>\Pr (X\geq 4.2)</math> 0.3085</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> 0.3721</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> 0.6170</p></li></ol>
+<li><p><math>\Pr \left( (X\leq 3.8)\cup (X\geq 4.2)\right)</math> {0.6170}</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></ol>
 = Footnotes =

@@ Line 2: / Line 2: @@
 <ol>
-<li><p>[L1,L2] If <math>X\sim N(0,1)</math> evaluate</p>
+<li><p><math>L1,L2</math> If <math>X\sim N(0,1)</math> evaluate</p>
 <ol>
-<li><p><math>\Pr (X\leq 0.23)</math></p></li>
+<li><p><math>\Pr (X\leq 0.23)</math> Solution: 0.5910</p></li>
-<li><p><math>\Pr (X\geq 0.23)</math></p></li>
+<li><p><math>\Pr (X\geq 0.23)</math> 0.4090</p></li>
-<li><p><math>\Pr (-0.5 \leq X \leq 1.84)</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>
+<li><p><math>L1,L2</math> 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></p></li>
+<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></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></p></li></ol>
+<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>
-<li><p>[L1,L2] If <math>X\sim N(4,0.16)</math> evaluate</p>
+<li><p><math>L1,L2</math> If <math>X\sim N(4,0.16)</math> evaluate</p>
 <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>
 <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 =

@@ Line 4: / Line 4: @@
 <li><p>[L1,L2] 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\leq 0.23)</math></p></li>
-<li><p><math>\Pr (X\geq 0.2)</math></p></li>
+<li><p><math>\Pr (X\geq 0.23)</math></p></li>
-<li><p><math>\Pr (-0.5 \leq X \leq 1.8)</math></p></li></ol>
+<li><p><math>\Pr (-0.5 \leq X \leq 1.84)</math></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>