The expected value of the random variable is 7
The probability distribution is given as:
x=2,3,4,5,6,7,8,9,10,11,12
Probability =1/36,1/18,1/12,1/9,5/36,1/6,5/36,1/9,1/12,1/18,1/36
The expected value of the random variable is calculated using
E(X) = ∑xP(x)
Using the above formula, we have
E(x) = 2 * 1/36 + 3 * 1/18 + 4 * 1/12 + 5 * 1/9+ 6 * 5/36 + 7 * 1/6 + 8 * 5/36 + 9 * 1/9 + 10 * 1/12 + 11 * 1/18+ 12 * 1/36
Evaluate the sum of products
E(x) = 7
Hence, the expected value of the random variable is 7
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