A collection of 30 gems, all of which are identical in appearance, are supposedto be genuine diamonds, but actually contain 8 worthless stones. The genuine diamonds arevalued at $1200 each. Two gems are selected. (a) Let X denote the total actual value of the gems selected. Find the probability distribution function for X.
(b) Find E(X).

Step-by-step explanation:

From the given information:

There are 30 collections of gems, of which 8 are worthless;

Thus, the number of the genuine diamonds = 30 - 8 = 22.

Let X = random variable;

X consider the value as 0 (for  2 worthless stone selection),

X = 1200(1 worthless stone  & 1 genuine stone)

X = 2400 (2 genuine stones selected)

However, the numbers of ways of selecting and chosen Gems can be estimated as:

Thus;

To find E(X):

E(X) = (0 × 0.0644) + (1200 × 0.4046)  + (2400 × 0.5310)

E(X) = 0 + 485.52 + 1274.4

E(X) = 1759.92

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