Question

Q) Let Xbe a discrete random variable representing the maximum value of the two numbers on

throwing two identical balanced dice for one time only. Then:
a) Find the possible values of the random variable X for the following cases:
b) Determine the probability mass function P (X = ·).
c) Draw the graphical representation of the probability mass function P (X = ·).
d) Determine the distribution functionF  .
			X
e) Sketch the functions in part (a).
f) Calculate the mean and variance for the random variable X.
g) Calculate the standard deviation ofX.
h) Calculate the standard deviation of the random variable Y:= 2X + 5 .

Answer 1

a)

possible values of the random variable X for the following cases: 1,2,3,4,5,6

b) probability mass function P(X=x)=(2n-1)/36

x	f(x)
1	1/36
2	1/12
3	5/36
4	7/36
5	1/4
6	11/36

c)

d)

x	F(x)
1	1/36
2	1/9
3	1/4
4	4/9
5	25/36
6	1

e)

f)

x	f(x)	xP(x)	x2P(x)
1	1/36	0.028	0.028
2	1/12	0.167	0.333
3	5/36	0.417	1.250
4	7/36	0.778	3.111
5	1/4	1.250	6.250
6	11/36	1.833	11.000
	total	4.472	21.972
	E(x) =μ=	ΣxP(x) =	4.4722
	E(x2) =	Σx2P(x) =	21.9722
	Var(x)=σ2 =	E(x2)-(E(x))2=	1.9715
	std deviation=	σ= √σ2 =	1.4041

mean of X=4.4722

variance =1.9715

g)std deviation =1.4041

h)

standard deviation of the random variable Y:=SD(2X+5)=2*SD(X)=2.8082