Question

12. The total number of heads for a coin flipped four times is a random variable X with the following probability distribution P(X-0) 0.0625 PX-1) 0.2500 P(X-2) 0.3750 POX-3) 0.2500 P(X-4) 0.0625 Draw a graph of the density function. 13. The total number of heads for a coin flipped four times is a random variable X with the following probability distribution. P(X-0) 0.10 P(X-1) 0.40 P(X-2) 0.20 P(X-3) 0.10 P(X-4) 0.20 Determine the mean and variance of x.

Answer 1

12)

13)

x	P(x)	xP(x)	x2P(x)
0	0.1	0.000	0.000
1	0.4	0.400	0.400
2	0.2	0.400	0.800
3	0.1	0.300	0.900
4	0.2	0.800	3.200
	total	1.900	5.300
	E(x) =μ=	ΣxP(x) =	1.9000
	E(x2) =	Σx2P(x) =	5.3000
	Var(x)=σ2 =	E(x2)-(E(x))2=	1.690

from above mean =1.90

and variance =1.69