Ex 13.4, 16
Last updated at Aug. 11, 2021 by Teachoo
Mean or Expectation of random variable
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Mean or Expectation of random variable
Ex 13.4, 16 The mean of the numbers obtained on throwing a die having written 1 on three faces, 2 on two faces and 5 on one face is (A) 1 (B) 2 (C) 5 (D) 83 Let, X be the number obtained on throwing the die Since on throwing a die, we can get 1, 2 or 5 Value of X can be 1, 2 or 5 So, The Probability are given by P(X = 1) = 𝑁𝑢𝑚𝑏𝑒𝑟 𝑓𝑎𝑐𝑒𝑠 1 𝑖𝑠 𝑤𝑟𝑖𝑡𝑡𝑒𝑛 𝑇𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑓𝑎𝑐𝑒𝑠 = 36 = 12 P(X = 2) = 𝑁𝑢𝑚𝑏𝑒𝑟 𝑓𝑎𝑐𝑒𝑠 2 𝑖𝑠 𝑤𝑟𝑖𝑡𝑡𝑒𝑛 𝑇𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑓𝑎𝑐𝑒𝑠 = 26 = 13 P(x = 5) = 𝑁𝑢𝑚𝑏𝑒𝑟 𝑓𝑎𝑐𝑒𝑠 5 𝑖𝑠 𝑤𝑟𝑖𝑡𝑡𝑒𝑛 𝑇𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑓𝑎𝑐𝑒𝑠 = 16 Hence the Probability distribution : The Mean of the number is given by 𝝁=𝑬 𝑿= 𝑖 = 1𝑛𝑥𝑖𝑝𝑖 = 1 × 12+2 × 13+ 5 × 16 = 12+ 23+ 56 = 3 + 4 + 56 = 126 = 2 Hence option B is correct