# Ex 13.4, 13 - Chapter 13 Class 12 Probability

Last updated at May 29, 2018 by Teachoo

Last updated at May 29, 2018 by Teachoo

Transcript

Ex 13.4, 13 Let X denote the sum of the numbers obtained when two fair dice are rolled. Find the variance and standard deviation of X. Here, X = Sum of numbers on two die Since pair of die are thrown, So, X can be 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 Thus, Probability distribution is Now, we need to find variance Var 𝑋 = 𝐸 𝑋2− 𝐸 𝑋2 Finding E(X) E(X) = 𝑖 = 1𝑛𝑥𝑖𝑝𝑖 = 2 × 136+3 × 236+4 × 336+5 × 436+6 × 536+7 × 636 +8 × 536+9 × 436+10 × 336+11 × 236+12 × 136 = 2 + 6 + 12 + 20 + 30 + 42 + 40 + 36 + 30 + 22 + 1236 = 252 36 = 7 Thus E(x) = 7 Finding E 𝑿𝟐 E 𝑿𝟐= 𝑖=1𝑛 𝑥2𝑖𝑃𝑖 = 22× 136 + 32× 236 + 42 × 336+ 52× 436+ 62× 536+ 72× 636 + 82 × 536+ 92× 436+ 102× 336+ 112 × 236+ 122× 136 = 4 + 18 + 48 + 100 + 180 + 294 + 320 + 324 + 300 + 242 + 14436 = 197436 = 𝟑𝟐𝟗𝟔 Now, Var 𝑿 = 𝑬 𝑿𝟐− 𝑬 𝑿𝟐 = 3296− 72 = 329 − 6 × 496 = 356 = 5.833 Standard deviation is given by 𝝈𝒙= 𝒗𝒂𝒓 𝑿 = 356 = 5.833 = 2.415

Chapter 13 Class 12 Probability

Serial order wise

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