

Mean or Expectation of random variable
Ex 13.4, 16 (MCQ) Deleted for CBSE Board 2022 Exams
Ex 13.4, 11 Important Deleted for CBSE Board 2022 Exams
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Ex 13.4, 12 Important Deleted for CBSE Board 2022 Exams You are here
Ex 13.4, 17 (MCQ) Important Deleted for CBSE Board 2022 Exams
Mean or Expectation of random variable
Ex 13.4, 12 Two numbers are selected at random (without replacement) from the first six positive integers. Let X denote the larger of the two numbers obtained. Find E(X).The first 6 positive integers are : 1, 2, 3, 4, 5, 6 And they are selected without replacement Let X : be the larger number of two numbers selected The possible outcomes are Sample space = S = {█(█((1, 2),(1, 3),(1, 4),(1, 5),(1, 6),@(2, 1),(2, 3),(2, 4),(2, 5),(2, 6),)@█((3, 1),(3, 2),(3, 4),(3, 5),(3, 6),@(4, 1),(4, 2),(4, 3),(4, 5),(4, 6),)@█((5, 1),(5, 2),(5, 3),(5, 4),(5, 6),@(6, 1),(6, 2),(6, 3),(6, 4),(6, 5) ))} Total number of possible outcomes = 30 The larger number can be : 2, 3, 4, 5 or 6 So, the values of X can be : 2, 3, 4, 5 or 6 Thus, the probability distribution is The mean Expected value is given by 𝝁=𝑬(𝑿)=∑_(𝑖=1)^𝑛▒𝑥𝑖𝑃𝑖 = 2 × 2/30+"3 × " 4/30+ 4 × 6/30+ 5 × 8/30+ 6 × 10/30 = (4 + 12 + 24 + 40 + 60)/30 = 140/30 = 𝟏𝟒/𝟑