Chapter 13 Class 12 Probability

Class 12
Important Questions for exams Class 12

Transcript

Question 15 In a meeting, 70% of the members favour and 30% oppose a certain proposal. A member is selected at random and we take X = 0 if he opposed, and X = 1 if he is in favour. Find E(X) and Var (X). Given that X = 0 is Members oppose X = 1 is members favour proposal Given, 70% of members favour proposal So, P(X = 1) = 70% = 0.7 and 30% of members oppose proposal So, P(X = 0) = 30% = 0.3 ∴ Probability distribution is The expectation value E(x) is given by : E 𝑿﷯ = 𝑖 = 1﷮𝑛﷮𝑥𝑖𝑝𝑖﷯ = 0 × 0.3 + 1 × 0.7 = 0.7 The variance of x is given by : Var 𝑋﷯=𝐸 𝑋﷮2﷯﷯− 𝐸 𝑋﷯﷯﷮2﷯ So, finding 𝐸 𝑋﷮2﷯﷯ E 𝑿﷮𝟐﷯﷯= 𝑖 = 1﷮𝑛﷮ 𝑥﷮𝑖﷯﷮2﷯𝑝𝑖﷯ = 02 × 0.3 + 12 × 0.7 = 0 + 0.7 = 0.7 Now, Var 𝒙﷯ = 𝐸 𝑥﷮2﷯﷯− 𝐸 𝑥﷯﷯﷮2﷯ = 0.7 – 0.7﷯﷮2﷯ = 0.7 1−0.7﷯ = 0.7 0.3﷯ = 0.21 Hence the expectation E(x) = 0.7 & variance var(x) = 0.21

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, Social Science, Physics, Chemistry, Computer Science at Teachoo.