Ex 13.4, 16 - Mean numbers obtained on throwing a die - Mean or Expectation of random variable

 Ex 13.4, 16 - Part 2
 Ex 13.4, 16 - Part 3

Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class


Transcript

Question 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) 8﷮3﷯ 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﷯ = 3﷮6﷯ = 1﷮2﷯ P(X = 2) = 𝑁𝑢𝑚𝑏𝑒𝑟 𝑓𝑎𝑐𝑒𝑠 2 𝑖𝑠 𝑤𝑟𝑖𝑡𝑡𝑒𝑛 ﷮𝑇𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑓𝑎𝑐𝑒𝑠﷯ = 2﷮6﷯ = 1﷮3﷯ P(x = 5) = 𝑁𝑢𝑚𝑏𝑒𝑟 𝑓𝑎𝑐𝑒𝑠 5 𝑖𝑠 𝑤𝑟𝑖𝑡𝑡𝑒𝑛 ﷮𝑇𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑓𝑎𝑐𝑒𝑠﷯ = 1﷮6﷯ Hence the Probability distribution : The Mean of the number is given by 𝝁=𝑬 𝑿﷯= 𝑖 = 1﷮𝑛﷮𝑥𝑖𝑝𝑖﷯ = 1 × 1﷮2﷯+2 × 1﷮3﷯+ 5 × 1﷮6﷯ = 1﷮2﷯+ 2﷮3﷯+ 5﷮6﷯ = 3 + 4 + 5﷮6﷯ = 12﷮6﷯ = 2 Hence option B is correct

Ask a doubt
Davneet Singh's photo - Co-founder, Teachoo

Made by

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.