Example 27 - Let random variable X be sum of numbers - Mean or Expectation of random variable

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  1. Chapter 13 Class 12 Probability
  2. Serial order wise
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Example 27 Let a pair of dice be thrown and the random variable X be the sum of the numbers that appear on the two dice. Find the mean or expectation of X. Since pair of die are thrown, Here, X = Sum of numbers on two die So, X can be 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 Thus, Probability distribution is Now, We need to find Mean or Expectation of X Mean or Expectation of X = 𝜇 = E(X) = 𝒊 = 𝟏﷮𝒏﷮𝒙𝒊𝒑𝒊﷯ = 2 × 1﷮36﷯+3 × 2﷮36﷯+4 × 3﷮36﷯+5 × 4﷮36﷯+6 × 5﷮36﷯+7 × 6﷮36﷯ +8 × 5﷮36﷯+9 × 4﷮36﷯+10 × 3﷮36﷯+11 × 2﷮36﷯+12 × 1﷮36﷯ = 2 + 6 + 12 + 20 + 30 + 42 + 40 + 36 + 30 + 22 + 12﷮36﷯ = 252 ﷮36﷯ = 7 × 36 ﷮36﷯ = 7 Thus mean or expectation is 7

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