![Cк3 1,2,..., n for k [3] A random variable K has probability distribution pK(k) (n[n+1])2 [a] What value of C will make this](http://img.homeworklib.com/questions/ce986240-9af3-11ec-968f-d1f0066c59b2.png?x-oss-process=image/resize,w_560)
A random variable K has probability distribution 
[a] What value of C will make this a discrete probability density?
[b] If n = 4, what is the E(K)?
Hint: Consider sums of powers of the first n integers.
Homework Answers
a) We use the property here that the sum of all probabilities for all the k values should be 1. Therefore, we get here:
Using the formula for the sum of cubes of n numbers, we have here:
Therefore, we have here:
therefore C = 4 is the required value of C here.
b) The expected value of K here is computed as:
Therefore 3.54 is the required expected value of k here.
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