Ex 13.4, 14 - A class has 15 students whose ages are 14, 17, 15 - Variance and Standard Deviation of a Random Variable

 Ex 13.4, 14 - Part 2
 Ex 13.4, 14 - Part 3
 Ex 13.4, 14 - Part 4
 Ex 13.4, 14 - Part 5

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Question 14 A class has 15 students whose ages are 14, 17, 15, 14, 21, 17, 19, 20, 16, 18, 20, 17, 16, 19 and 20 years. One student is selected in such a manner that each has the same chance of being chosen and the age X of the selected student is recorded. What is the probability distribution of the random variable X? Find mean, variance and standard deviation of X. Let X be the age of student selected The age of student selected can be 14, 17, 15, 21, 19, 16, 18, 20 So, X can have the value 14, 15, 16, 17, 18, 19, 20, 21 The Probability distribution is given by : The Mean is given by : E = =1 =14 2 15 +15 1 15 +16 2 15 +17 3 15 +18 1 15 +19 2 15 +20 3 15 +21 1 15 = 28 + 15 + 32 + 51 + 18 + 38 + 60 + 21 15 = 263 15 = 17.53 Hence the mean is 17.53 The variance of x is given by : Var = 2 2 So, finding 2 E = = 1 2 = 14 2 2 15 + 15 2 1 15 + 16 2 2 15 + 17 2 3 15 + 18 2 1 15 + 19 2 2 15 + 20 2 3 15 + 21 2 1 15 = 196 2 + 225 1+256 2+289 3+324 1+361 2+400 3+441 1 15 = 392 + 225 + 512 + 867 + 324 + 722 + 1200 + 441 15 = Now, Var = = 4683 15 263 15 2 = 4683 15 69169 225 = 4683 15 69169 225 = 70245 69169 225 = 1076 225 = 4.78 Standard deviation is given by = ( ) = . = 2.18

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo