Chapter 13 Class 12 Probability

Class 12
Important Questions for exams Class 12

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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) = ∑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

#### Davneet Singh

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.