Question

An overseas shipment of 5 foreign automobiles contains 2 that have slight
paint blemishes. If an agency receives 3 of these automobiles at random,
find the probability distribution of the random variable X representing the
number of automobiles with paint blemishes purchased by the agency.
Find the mean number of automobiles with paint blemishes.
Also calculate the variation

Answer 1

An overseas shipment of 5 foreign automobiles contains 2 that have slight paint blemishes. If an agency receives 3 of these automobiles at random, find the probability distribution of the random variable $X$ representing the number of automobiles with paint blemishes purchased by the agency. Find the mean number of automobiles with paint blemishes. Also, calculate the variation.

Answer

Let letter B represent blemished automobiles and U represent the non-blemished ones. Since 3 automobiles are picked at random, here is the sample space:

Therefore, the probability distribution will be as follows:

$$f (0) = \frac {\binom {3} {3} \binom {2} {0}}{\binom {5} {3}} = \frac {1}{1 0}$$ $$f (1) = \frac {\binom {3} {2} \binom {2} {1}}{\binom {5} {3}} = \frac {6}{1 0}$$ $$f (2) = \frac {\binom {3} {1} \binom {2} {2}}{\binom {5} {3}} = \frac {3}{1 0}$$

Mean number of automobiles with paint blemishes $= 5^{*}\frac{3}{10} = 1.5 \equiv 1$ automobile

The variation $= 5^{*}\frac{3}{10} *(1 - \frac{3}{10}) = 1.05 \equiv 1$ automobile

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