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Ex 13.4, 16 - Mean numbers obtained on throwing a die - Mean or Expectation of random variable

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  1. Chapter 13 Class 12 Probability
  2. Serial order wise
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Ex 13.4, 16 The mean of the numbers obtained on throwing a die having written 1 on three faces, 2 on two faces and 5 on one face is (A) 1 (B) 2 (C) 5 (D) 8๏ทฎ3๏ทฏ Let, X be the number obtained on throwing the die Since on throwing a die, we can get 1, 2 or 5 Value of X can be 1, 2 or 5 So, The Probability are given by P(X = 1) = ๐‘๐‘ข๐‘š๐‘๐‘’๐‘Ÿ ๐‘“๐‘Ž๐‘๐‘’๐‘  1 ๐‘–๐‘  ๐‘ค๐‘Ÿ๐‘–๐‘ก๐‘ก๐‘’๐‘› ๏ทฎ๐‘‡๐‘œ๐‘ก๐‘Ž๐‘™ ๐‘›๐‘ข๐‘š๐‘๐‘’๐‘Ÿ ๐‘œ๐‘“ ๐‘“๐‘Ž๐‘๐‘’๐‘ ๏ทฏ = 3๏ทฎ6๏ทฏ = 1๏ทฎ2๏ทฏ P(X = 2) = ๐‘๐‘ข๐‘š๐‘๐‘’๐‘Ÿ ๐‘“๐‘Ž๐‘๐‘’๐‘  2 ๐‘–๐‘  ๐‘ค๐‘Ÿ๐‘–๐‘ก๐‘ก๐‘’๐‘› ๏ทฎ๐‘‡๐‘œ๐‘ก๐‘Ž๐‘™ ๐‘›๐‘ข๐‘š๐‘๐‘’๐‘Ÿ ๐‘œ๐‘“ ๐‘“๐‘Ž๐‘๐‘’๐‘ ๏ทฏ = 2๏ทฎ6๏ทฏ = 1๏ทฎ3๏ทฏ P(x = 5) = ๐‘๐‘ข๐‘š๐‘๐‘’๐‘Ÿ ๐‘“๐‘Ž๐‘๐‘’๐‘  5 ๐‘–๐‘  ๐‘ค๐‘Ÿ๐‘–๐‘ก๐‘ก๐‘’๐‘› ๏ทฎ๐‘‡๐‘œ๐‘ก๐‘Ž๐‘™ ๐‘›๐‘ข๐‘š๐‘๐‘’๐‘Ÿ ๐‘œ๐‘“ ๐‘“๐‘Ž๐‘๐‘’๐‘ ๏ทฏ = 1๏ทฎ6๏ทฏ Hence the Probability distribution : The Mean of the number is given by ๐=๐‘ฌ ๐‘ฟ๏ทฏ= ๐‘– = 1๏ทฎ๐‘›๏ทฎ๐‘ฅ๐‘–๐‘๐‘–๏ทฏ = 1 ร— 1๏ทฎ2๏ทฏ+2 ร— 1๏ทฎ3๏ทฏ+ 5 ร— 1๏ทฎ6๏ทฏ = 1๏ทฎ2๏ทฏ+ 2๏ทฎ3๏ทฏ+ 5๏ทฎ6๏ทฏ = 3 + 4 + 5๏ทฎ6๏ทฏ = 12๏ทฎ6๏ทฏ = 2 Hence option B is correct

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.
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