Question 7 - Chapter 13 Class 12 Probability (Important Question)

Last updated at April 16, 2024 by Teachoo

Example 28 - Find variance of number obtained on throw of die

Example 28 - Chapter 13 Class 12 Probability - Part 2

Example 28 - Chapter 13 Class 12 Probability - Part 3

Transcript

Question 7 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) = ∑2_(𝒊 = 𝟏)^𝒏▒𝒙𝒊𝒑𝒊 = 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 (𝑿)=𝑬(𝑿^𝟐 )−[𝑬(𝑿)]^𝟐 So, finding 𝐸(𝑋^2 ) E(𝑋^2 )=∑2_(𝑖 = 1)^𝑛▒〖〖𝑥_𝑖〗^2 𝑝𝑖〗 = 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 (𝑋)=𝐸(𝑋^2 )−[𝐸(𝑋)]^2 = 91/6−[21/6]^2 = 91/6−441/36 = (546 − 441)/36 = 105/36 = 35/12 Hence, variance is 𝟑𝟓/𝟏𝟐

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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