Example 28 - Find variance of number obtained on throw of die - Variance and Standard Deviation of a Random Variable

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Slide44.JPG

  1. Chapter 13 Class 12 Probability
  2. Serial order wise

Transcript

Example 28 Find the variance of the number obtained on a throw of an unbiased die. Let X be number obtained on a throw So, value of X can be 1, 2, 3, 4, 5 or 6 Since die unbiased, Probability of getting of each number is equal P(X = 1) = P(X = 2) = P(X = 3) = P(X = 4) = P(X = 5) = P(X = 6) = 1 6 Hence, probability distribution The mean Expectation value is given by E(X) = = = 1 1 6 +2 1 6 + 3 1 6 + 3 1 6 + 5 1 6 + 6 1 6 = 21 6 The variance of x is given by : Var = So, finding 2 E 2 = = 1 2 = 12 1 6 +22 1 6 + 32 1 6 + 42 1 6 + 52 1 6 + 62 1 6 = 1 + 4 + 9 + 16 + 25 + 36 6 = 91 6 Now, Var = 2 2 = 91 6 21 6 2 = 91 6 441 36 = 546 441 36 = 105 36 = 35 12 Hence, variance is

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