Lab 1

Part 2: Length of Longest Run

Table 5: Largest run

	1	2	3	4	5	6	7	8	9	10
Row 1	4	4	6	4	9	8	4	5	6	4
Row 2	4	4	4	5	5	5	4	4	4	4
Row 3	6	6	4	6	6	4	8	7	5	5
Row 4	5	4	6	4	6	4	6	8	5	5
Row 5	5	3	6	4	4	5	6	4	10	4
Row 6	4	5	3	3	3	3	3	9	6	7
Row 7	7	4	5	4	6	5	4	4	5	6
Row 8	5	4	4	5	3	8	5	4	3	3
Row 9	7	7	5	6	6	6	5	4	8	5
Row 10	4	5	8	5	5	4	3	4	5	6

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1 Histograms

• Histogram 1 (manual):
  • 
• Histogram 2
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2 Box-plots

• manual
  • 
• full
  • 

3 Mean and Standard Deviation

$$\bar{L}=\frac{1}{100}\sum _{i=1}^{100}{L}_i=5.06,s=\sqrt{\frac{{\sum }_{i=1}^{100}(L_i-\bar{L}{)}^2}{99}}=1.49$$

4 Empirical PMF

$L$	3	4	5	6	7	8	9	10
Frequency $f_L$	10	33	25	18	5	6	2	1
Probability $P(L=\ell )=f_L/100$	0.10	0.33	0.25	0.18	0.05	0.06	0.02	0.01

${\sum }_{\ell }P(L=\ell )=1.00$

5 95 % Percentile

Sort the 100 values → rank $(r=0.95(100+1)=95.95)$.
Both the 95th and 96th sorted values are 8
$L_{0.95}=8$