SOLUTION: 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

Question 1087060: 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
Answer by mathmate(429) (Show Source): You can put this solution on YOUR website!
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]

RELATED QUESTIONS
Suppose a fair coin is tossed three times. Let X be the random variable that represents... (answered by yurtman,ikleyn)

A fair coin is tossed 10 times. Let X denote the number of heads obtained. Find the... (answered by ewatrrr)

A fair coin is tossed three times. Let X be the number of heads in the tosses minus the... (answered by Edwin McCravy)

a fair coin is tossed four times, let x be the product of the number of heads times the... (answered by stanbon)

Consider the event of getting a head in 4tosses of a fair coin. Let X be the random... (answered by greenestamps,math_tutor2020)

3. Four coins are tossed. Let Y be the random variable representing the number of heads... (answered by ikleyn)

Q1) Three fair coins are tossed. The number of heads obtained is recorded a] Write... (answered by stanbon)

if a fair coin is tossed 100 times, find the mean and the standard deviation for the... (answered by mananth)

Let random variable x represent the number of heads when a fair coin is tossed three... (answered by Edwin McCravy)