Ex 13.4, 13 - Let X denote sum of numbers obtained when 2

Ex 13.4, 13 - Chapter 13 Class 12 Probability - Part 2
Ex 13.4, 13 - Chapter 13 Class 12 Probability - Part 3 Ex 13.4, 13 - Chapter 13 Class 12 Probability - Part 4 Ex 13.4, 13 - Chapter 13 Class 12 Probability - Part 5 Ex 13.4, 13 - Chapter 13 Class 12 Probability - Part 6

  1. Chapter 13 Class 12 Probability (Term 2)
  2. Serial order wise

Transcript

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‘‹) "= " ๐ธ(๐‘‹^2 )โˆ’[๐ธ(๐‘‹)]^2 Finding E(X) E(X) = โˆ‘_(๐‘– = 1)^๐‘›โ–’๐‘ฅ๐‘–๐‘๐‘– = 2 ร—1/36+3 ร— 2/36+4 ร— 3/36+5 ร—4/36+6 ร— 5/36+7 ร— 6/36 +8 ร— 5/36+9 ร— 4/36+10 ร—3/36+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(๐‘ฟ^๐Ÿ ) E(๐‘ฟ^๐Ÿ )=โˆ‘_(๐‘–=1)^๐‘›โ–’ใ€–๐‘ฅ^2 ๐‘–๐‘ƒ๐‘–ใ€— = 2^2ร—1/36 +3^2ร—2/36 +4^2 ร—3/36+5^2ร—4/36+6^2ร—5/36+7^2ร— 6/36 +8^2 ร—5/36+9^2ร— 4/36+ใ€–10ใ€—^2ร—3/36+ใ€–11ใ€—^2 ร—2/36+ใ€–12ใ€—^2ร—1/36 = (4 + 18 + 48 + 100 + 180 + 294 + 320 + 324 + 300 + 242 + 144)/36 = 1974/36 = ๐Ÿ‘๐Ÿ๐Ÿ—/๐Ÿ” Now, Var (๐‘ฟ) "= " ๐‘ฌ(๐‘ฟ^๐Ÿ )โˆ’[๐‘ฌ(๐‘ฟ)]^๐Ÿ = 329/6โˆ’(7)^2 = (329 โˆ’ 6 ร— 49)/6 = 35/6 = 5.833 Standard deviation is given by ๐ˆ_๐’™=โˆš(๐’—๐’‚๐’“ (๐‘ฟ) ) =โˆš(35/6) =โˆš5.833 = 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

About the Author

Davneet Singh's photo - Teacher, Engineer, Marketer
Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.