Question

Let X be the random variable representing the difference between the number of headsand the number of tails obtained when a fair coin is tossed 4 times.

a) What are the possible values of X?

b) Compute all the probability distribution of X?

c) Draw the cumulative distribution function F(x) of the random variable X.

Answer 1

a)possible values of X are -4,-2,0,2,4.

b) below is  probability distribution of X:

P(X=-4)=P(0 heads and 4 tails)= =1/16

P(X=-2)=P(1 heads and 3 tails)= =4/16=1/4

P(X=0)=P(2 heads and 2 tails)= =6/16=3/8

P(X=2)=P(3 heads and 1 tails)= =4/16=1/4

P(X=4)=P(4 heads and 0 tails)==1/16

c)

from above below is CDF of X:

	0		x<-4
	1/16		-4<=x<-2
F(X)=	5/16	for	-2<=x<0
	11/16		0<=x<2
	15/16		2<=x<4
	1		x>=4