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Question

For what value of k the following distribution is a probability distribution?
X = xi : 0 1 2 3
P (X = xi) : 2k4 3k2 − 5k3 2k − 3k2 3k − 1

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Solution

We know that the sum of probabilities in a probability distribution is always 1.

∴ P (X = 0) + P (X = 1) + P (X = 2) + P (X = 3) = 1

2k4+3k2-5k3+2k-3k2+3k-1=12k4-5k3+5k=22k4-5k3+5k-2=0k-1k-22k2+k-1=0k-1k-22k-1k+1=0k=-1 , 12, 1, 2Neglecting -1 , 1 and 2 as they give the value of probability negative or greater than 1

∴ k =12

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