Slide12.JPG

Slide13.JPG
Slide14.JPG
Slide15.JPG
Slide16.JPG

Go Ad-free

Transcript

Example 4 Let a sample space be S = {ω1, ω2,..., ω6}.Which of the following assignments of probabilities to each outcome are valid? Outcomes ω 1 ω 2 ω 3 ω 4 ω 5 ω 6 (a) 1/6 1/6 1/6 1/6 1/6 1/6 S = { ω1, ω2, ω3, ω4, ω5, ω6,} Sum of probability = ω1 + ω2 + ω3 + ω4 + ω5 + ω6 = 1/6 + 1/6 + 1/6 + 1/6 + 1/6 + 1/6 = 6/6 = 1 ∴ Assignment of probability is valid Example 4 Outcomes ω1 ω 2 ω 3 ω 4 ω 5 ω 6 (b) 1 0 0 0 0 0 \ Sum of probability = ω1 + ω2 + ω3 + ω4 + ω5 + ω6 = 1 + 0 + 0 + 0 + 0 + 0 + 0 = 1 ∴ Assignment of probability is valid Example 4 Outcomes ω1 ω 2 ω 3 ω 4 ω 5 ω 6 (c) 1/8 2/3 1/3 1/3 – 1/4 – 1/3 Probability of any event cannot be negative Hence, this assignment of probability is not valid Example 4 Outcomes ω1 ω 2 ω 3 ω 4 ω 5 ω 6 (d) 1/12 1/12 1/6 1/6 1/6 3/2 Probability 3/2 is greater than 1 But, Probability cannot be greater than 1 Hence, this assignment of probability is not valid Example 4 Outcomes ω1 ω 2 ω 3 ω 4 ω 5 ω 6 (e) 0.1 0.2 0.3 0.4 0.5 0.6 Sum of probability = ω1 + ω2 + ω3 + ω4 + ω5 + ω6 = 0.1 + 0.2 + 0.3 + 0.4 + 0.5 + 0.6 = 2.1 Sum of probability is greater than 1 ∴ This assignment of probability is not valid

Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo