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महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता १२ वी

Find the mean of number randomly selected from 1 to 15. - Mathematics and Statistics

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प्रश्न

Find the mean of number randomly selected from 1 to 15.

बेरीज
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उत्तर

The sample space of the experiment is S = {1, 2, 3, …, 15}.

Let X denotes the number selected.

Then X is a random variable that can take values 1, 2, 3, …, 15.

Each number selected is equiprobable therefore

P(1) = P(2) = P(3) = … = P(15) = `1/15`

μ = E(X) = `sum_(i = 1)^n x_ip_i`

= `1 xx 1/15 + 2 xx 1/15 + 3 xx 1/15 + ... + 15 xx 1/15`

= `(1 + 2 + 3 + ... + 15) xx 1/15`

= `((15 xx 16)/2) xx 1/15`

= 8

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