Answer :

To find the value of k we will be using the very basic idea of probability.


Note: We know that the sum of the probabilities of all random variables taken from a given sample space is equal to 1.


P(X=0.5) + P(X=1) + P(X=1.5) + P(X=2) = 1


k + k2 + 2k2 + k = 1


3k2 + 2k – 1 = 0


3k2 + 3k - k – 1 = 0


3k(k+1) – (k+1) = 0


(3k-1)(k+1) = 0


k = 1/3 or k = -1


k represents probability of an event. Hence 0≤P(X)≤1


k = 1/3


Mean of any probability distribution is given by- Mean = ∑xipi


Now we have,


X: 0.5 1 1.5 2


P(X): 1/3 1/9 2/9 1/3


first we need to find the product i.e. pixi and add them to get mean.


Mean = 0.5 x (1/3) + 1 x (1/9) + 1.5 x (2/9) +2 x (1/3)



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