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Last updated at Feb. 15, 2020 by Teachoo

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Ex 13.4, 13 Let X denote the sum of the numbers obtained when two fair dice are rolled. Find the variance and standard deviation of X.Ex 13.4, 13 Let X denote the sum of the numbers obtained when two fair dice are rolled. Find the variance and standard deviation of X.Thus, Probability distribution is Now, we need to find variance Var (๐) "= " ๐ธ(๐^2 )โ[๐ธ(๐)]^2 Finding E(X) E(X) = โ_(๐ = 1)^๐โ๐ฅ๐๐๐ = 2 ร1/36+3 ร 2/36+4 ร 3/36+5 ร4/36+6 ร 5/36+7 ร 6/36 +8 ร 5/36+9 ร 4/36+10 ร3/36+11 ร 2/36+12 ร 1/36 = (2 + 6 + 12 + 20 + 30 + 42 + 40 + 36 + 30 + 22 + 12)/36 = (252 )/36 = 7 Thus E(x) = 7 Finding E(๐ฟ^๐ ) E(๐ฟ^๐ )=โ_(๐=1)^๐โใ๐ฅ^2 ๐๐๐ใ = 2^2ร1/36 +3^2ร2/36 +4^2 ร3/36+5^2ร4/36+6^2ร5/36+7^2ร 6/36 +8^2 ร5/36+9^2ร 4/36+ใ10ใ^2ร3/36+ใ11ใ^2 ร2/36+ใ12ใ^2ร1/36 = (4 + 18 + 48 + 100 + 180 + 294 + 320 + 324 + 300 + 242 + 144)/36 = 1974/36 = ๐๐๐/๐ Now, Var (๐ฟ) "= " ๐ฌ(๐ฟ^๐ )โ[๐ฌ(๐ฟ)]^๐ = 329/6โ(7)^2 = (329 โ 6 ร 49)/6 = 35/6 = 5.833 Standard deviation is given by ๐_๐=โ(๐๐๐ (๐ฟ) ) =โ(35/6) =โ5.833 = 2.415 43 ร 3 = 129 44 ร 4 = 176 45 ร 5 = 225 4824 ร 4 = 19296 4825 ร 5 = 24125 4826 ร 6 = 28956

Ex 13.4

Ex 13.4, 1

Ex 13.4, 2

Ex 13.4, 3 Important

Ex 13.4, 4

Ex 13.4, 5

Ex 13.4, 6 Important

Ex 13.4, 7 Important

Ex 13.4, 8

Ex 13.4, 9

Ex 13.4, 10 Not in Syllabus - CBSE Exams 2021

Ex 13.4, 11 Important Not in Syllabus - CBSE Exams 2021

Ex 13.4, 12 Important Not in Syllabus - CBSE Exams 2021

Ex 13.4, 13 Important Not in Syllabus - CBSE Exams 2021 You are here

Ex 13.4, 14 Not in Syllabus - CBSE Exams 2021

Ex 13.4, 15 Not in Syllabus - CBSE Exams 2021

Ex 13.4, 16 Not in Syllabus - CBSE Exams 2021

Ex 13.4, 17 Important Not in Syllabus - CBSE Exams 2021

Chapter 13 Class 12 Probability

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About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.