X is a discrete random variable with probability mass function p ( x ) = c x 2 for x = 1 2 , 1 , 3 2 , 2 . Find the value of c. Find the expected value of X

fro x = 12, 1, 32, 2 if the set of x is different just follow the same procedure for your particular set.

c = 1/1173

E[x] = 29.416

Step-by-step explanation:

The probability mass function is the probability that a discrete random variable X  takes a particular value of x for the probability mass function the sum of all the items in the mass function should be equal one, therefore, 1 = c(12^2 + 1^2 + 32^2 + 2^2) = 1, solving for c we get c = 1/1173, our probability mass function is p(x) = 1/1172*x^2 for x = 12, 1, 32, 2

The expected value is the probability-weighted average of all possible values, to calculate it we need to sum each item x by its respective probability:

E[X] = 12*(1/1173*12^2)+1*(1/1173*1^2)+32(1/1173*32^2)+2(1/1173*2^2) = 29.416

Please note that to calculate E[X] we need to calculate c first to have the probabilities of each x

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