SOLUTION: A discrete random variable X has a pdf of the form f(x) = c(8 - x) for x = 0, 1, 2, 3, 4, 5, and zero otherwise. (a) Find the constant c. (b) Find the CDF, F(x). (c) Find P[X >

n              f(n)
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0  c(8 - 0) = 8c         = 8/33
1  c(8 - 1) = 7c         = 7/33
2  c(8 - 2) = 6c         = 6/33 
3  c(8 - 3) = 5c         = 5/33
4  c(8 - 4) = 4c         = 4/33
5  c(8 - 5) = 3c         = 3/33
-------------------------------
      total = 33c = 1       
                c = 1/33

n                                  F(n)
----------------------------------------
0  F(0) = f(0) = 8/33
1  F(1) = F(0)+f(1) =  8/33+7/33 = 15/33
2  F(2) = F(1)+f(2) = 15/33+6/33 = 21/33 
3  F(3) = F(2)+f(3) = 21/33+5/33 = 26/33
4  F(4) = F(3)+f(4) = 26/33+4/33 = 30/33
5  F(5) = F(4)+f(5) = 30/33+3/33
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P[X > 2] = P[X = 3] + P[X = 4] + P[X = 5] = 5/33 + 4/33 + 3/33 = 12/33 = 4/11

or you could do it this way if there were very many fewer this way:

P[X > 2] = 1 - P[x < F(2) = 1 - 21/33 = 33/33 - 21/33 = 12/33 = 4/11

 



Edwin