b

Question 1: Probability Concepts and application [20]

1.1.Consider the following random statement: "I'm 110% sure that I will complete my degree in 2022" Using the basic laws of probability, explain why the latter statement is either true or false. (1)

1.2.What are the 3 ways that are mainly used in statistical application to represent the probability distribution of a random variable? (1)

1.3.Consider the following:

a)

x	2	3	4	6
()	0.15	0.20	0.40	0.35

x	0	1	2	3
()	0.2	0.3	0.3	0.2

c)

x	-2	-1	0
()	0.25	0.50	0.20

d)

x	4	9	20
()	-0.3	1.0	0.3

(i) Explain why each of the above (i.e. a. to d.) is or is not a valid probability distribution.

(ii) Draw the histogram of the valid probability distribution(s) using MS Excel or any other software of your choice and comment on the skewness of the distribution