Check whether the following are valid Probability Mass Funct

Check whether the following are valid Probability Mass Function or Probability Density Function.

f(x) = (x – 2) / 2 for x = 1, 2, 3, and 4

f(x) = x² / 25 for x= 0, 1, 2, 3, and 4

f(x) = (x + 1) / 14 for x = 1, 2, 3, and 4

f(x) = (x-2)/2 x = 1,2,3,4

So, for x = 1 f(1) = -1/2 <0 so f(x) = (x-2)/2 is not a PDF.

f(x) =(x + 1) / 14 f(x)>=0 for all values of x

Now f(1) + f(2)+f(3)+f(4) = (1+1)/14 + (2+1)/14 + (3+1)/14 + (4+1)/14 = (2+ 3 + 4+ 5) /14 = 14/14 = 1

Hence satisfying all conditions for PDF.