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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

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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) = βˆ‘2_(π’Š = 𝟏)^π’β–’π’™π’Šπ’‘π’Š = 1 Γ— 1/6+2 Γ— 1/6+ 3 Γ— 1/6+ 3 Γ— 1/6+ 5 Γ— 1/6+ 6 Γ— 1/6 = 21/6 The variance of x is given by : Var (𝑿)=𝑬(𝑿^𝟐 )βˆ’[𝑬(𝑿)]^𝟐 So, finding 𝐸(𝑋^2 ) E(𝑋^2 )=βˆ‘2_(𝑖 = 1)^𝑛▒〖〖π‘₯_𝑖〗^2 𝑝𝑖〗 = 12 Γ— 1/6+22 Γ— 1/6+ 32 Γ— 1/6+ 42 Γ— 1/6+ 52 Γ— 1/6+ 62 Γ— 1/6 = (1 + 4 + 9 + 16 + 25 + 36)/6 = 91/6 Now, Var (𝑋)=𝐸(𝑋^2 )βˆ’[𝐸(𝑋)]^2 = 91/6βˆ’[21/6]^2 = 91/6βˆ’441/36 = (546 βˆ’ 441)/36 = 105/36 = 35/12 Hence, variance is πŸ‘πŸ“/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 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.