Question

Could you please show me how to calculate the probability density function (pdf) e.g. the scaled frequency. You will need to give the absolute frequency, relative frequency and the
scaled frequency of the values below. Please show all working out. Please only answer if you are 100% sure you can solve it accurately and provide all of the correct working out.

Thank you

force (kN)                                                   Distance (m)      

2.11                                                                    2.33

2.33                                                                   3.42

3.02                                                                  3.13

3.02                                                                   1.32

7.83                                                                   0.53

4.40                                                                   4.12

1.48                                                                   3.67

1.40                                                                   4.98

4.81                                                                  2.34

1.53                                                                  1.04

Answer 1

Given Data set

	force	Distance(m)
	2.11	2.33
	2.33	3.42
	3.02	3.13
	3.02	1.32
	7.83	0.53
	4.4	4.12
	1.48	3.67
	1.4	4.98
	4.81	2.34
	1.53	1.04
N	10	10
min	1.4	0.53
max	7.83	4.98
1+3.222*log10(N)	4.222	4.222
no of classes taken	5	5
Range	6.43	4.45
	6.44	4.46
Classes width	1.288	0.892

From the given information at first find minimum,maximum,range , class width and non overlapping classes.

Then by counting prepare the following frequency table which provides cell frequency, scaled frequency, relative frequency or pdf and marginal probability

force	Count of force
1.4-2.69	5
2.69-3.98	2
3.98-5.27	2
6.56-7.85	1
Grand Total	10
distance	Count of Distance(m)
0.53-1.43	3
2.33-3.23	3
3.23-4.13	3
4.13-5.03	1
Grand Total	10

	Bivariate frequency table
				Distance			Total or scaled frequency
		0.53-1.43	1.43-2.33	2.33-3.23	3.23-4.13	4.13-5.03
	1.4-2.69	1		1	2	1	5
	2.69-3.98	1		1			2
force	3.98-5.27			1	1		2
	5.27-6.56						0
	6.56-7.85	1					1
	Total or scaled frequency	3	0	3	3	1	10

	Relative frquency or probability density table
				Distance			Marginal prob
		0.53-1.43	1.43-2.33	2.33-3.23	3.23-4.13	4.13-5.03
	1.4-2.69	0.1	0	0.1	0.2	0.1	0.5
	2.69-3.98	0.1	0	0.1	0	0	0.2
force	3.98-5.27	0	0	0.1	0.1	0	0.2
	5.27-6.56	0	0	0	0	0	0
	6.56-7.85	0.1	0	0	0	0	0.1
	Marginal prob.	0.3	0	0.3	0.3	0.1	1