Q. 14

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Given : Four rotten oranges are mixed with 16 good ones. Three oranges are drawn one by one without replacement.

To find : mean (๐) and variance (ฯ2)

Formula used :

Mean = E(X) =

Variance = E(X2) -

Mean = E(X) = = x1P(x1) + x2P(x2) + x3P(x3)

Four rotten oranges are mixed with 16 good ones. Three oranges are drawn one by one without replacement.

Let X denote the number of rotten oranges drawn

There are 4 rotten oranges present in 20 oranges

P(0) = = =

P(1) = = =

P(2) = = =

P(3) = = =

The probability distribution table is as follows,

Mean = E(X) = 0() + 1() + 2() + 3() = 0 + + + =

Mean = E(X) = =

= =

E(X2) = = P(x1) + P(x2) + P(x3)

E(X2) = () + () + () + () = 0 + + + =

E(X2) = =

Variance = E(X2) - = โ = =

Variance = E(X2) - =

Mean = E(X) =

Variance =

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