Probability and Statistics Lecture 17

Continued

Probability and Statistics Lecture 16 Prerequisites

• CoVariance
• Karl Pearson’s Correlation Coefficient
• Spearman’s Correlation Coefficient

Co variance

Covariance is a measure of how much two random variables change together. It measures the direction of the linear relationship between two variables. It is calculated as the expected value of the product of the deviations of two random variables from their respective expected values.

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Questions

Question 1 Based on Karl Pearsons coefficient

to find $\bar{x}$

X	Y	$X-\bar{X}$	$Y-\bar{Y}$	$(X-\bar{X})(Y-\bar{Y})$	x
28	23	-8	-8	64	64	64
45	34	9	3	27	81	9
40	33	4	2	8	16	4
38	34	2	3	6	4	9
35	30	-1	-1	1	1	1
33	26	-3	-5	15	9	25
40	28	4	-3	-12	16	9
32	31	-4	0	0	16	0
36	36	0	5	0	0	25
33	35	-3	4	-12	9	16

Question 2 Based on Spearmans coefficient

X	18	20	34	52	12
Y	39	23	35	18	48

X	Y	$X-\bar{X}$	$Y-\bar{Y}$	$(X-\bar{X})(Y-\bar{Y})$	$D$	$D^2$

References

Information

• date: 2025.02.21
• time: 11:12

Continued

Probability and Statistics Lecture 18