Question

Given the set of random variables and their associated probabilities, This is a Probability
Distribution because the probabilities add up to 1.
X P(x)3
0 1/16
1 4/16
2 6/16
3 4/16
4 1/16

∑P(x) = 16/16 =1

Find the Mean μ of this probability distribution and standard deviation ð of the distribution.

Answer 1

x	P(X=x)	xP(x)	x2P(x)
0	1/16	0.00000	0.00000
1	1/4	0.25000	0.25000
2	3/8	0.75000	1.50000
3	1/4	0.75000	2.25000
4	1/16	0.25000	1.00000
total	1.00	2.0000	5.0000
	E(x) =μ=	ΣxP(x) =	2.0000
	E(x2) =	Σx2P(x) =	5.0000
	Var(x)=σ2 =	E(x2)-(E(x))2=	1.000000
	std deviation=	σ= √σ2 =	1.00000

Mean μ of this probability distribution E(x)=2.00

standard deviation ð of the distribution =1.00