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Here we are given the values of x and we are also given the probability with which each of the values occur. To find the mean of the random variable x, we have to multiply each of the values with their respective probability and find the sum of all the products. The sum that we find by doing this is the required mean.
So we have a probability of 0.4 for $ 2, 0.2 for $14, 0.2 for $20 and 0.2 for $100
Therefore 2*0.4 + 14*0.2 + 20*0.2 + 100*0.2
= .8 + 2.8 + 4 + 20 = 27.6
Therefore the required mean of the random variable is 27.6
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