<PRE><B>Question 1087060</B>
Question:
A fair coin is tossed four times, let x be a random variable representing the number of heads, find the p.d.f and the c.d.f of x   
 
Solution:
A fair coin tossed four times has 2^4=16 outcomes.  Each outcome belongs to one of 5 distinct events: sum of number of heads={0,1,2,3,4}.
By a tree diagram, or a table:
HHHHHHHHTTTTTTTT
HHHHTTTTHHHHTTTT
HHTTHHTTHHTTHHTT
HTHTHTHTHTHTHTHT
4332322132212110
so frequency table can be made:
Sum frequency
4 1
3 4
2 6
1 4
0 1
The result of which is not a surprise for those who have worked with binomial theorem or the Pascal Triangle.

So the pdf is simply {1/16,4/16,6/16,4/16,1/16} for x=[0,4]
and the cdf is the cumulative sum, namely {1/16,5/16,11/16,15/16,16/16} for x=[0,4]

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