Question

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

A random variable K has probability distribution image.png

[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.

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Answer #1

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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