Question

10. Let X denote the number of times a certain numerical control machine will malfunction: 1, 2, or 3 times on any given day. Let Y denote the number of times a technician is called on an emergency call. Their joint probability distribution is given as 0.05 0.10 0.20 Evaluate the marginal distribution of X. flx, y) 1 1 0.05 y 3 0.05 5 0.00 0.10 0.35 0.10 a. b. Evaluate the marginal distribution of Y c. Find eXY-3/X -2). d. Are the two Random Variables X and Yindependent? Justify your answer.

Answer 1

from above :joint distribution of X and Y is as follows:

a)

	x
y	1	2	3	Total
1	0.0500	0.0500	0.1000	0.2000
3	0.0500	0.1000	0.3500	0.5000
5	0.0000	0.2000	0.1000	0.3000
Total	0.1000	0.3500	0.5500	1.0000

a)

from above marginal distribution of X is as follows:

x	P(x)
1	0.1000
2	0.3500
3	0.5500

b)

marginal distribution of Y is as follows:\

y	P(y)
1	0.2000
3	0.5000
5	0.3000

c)P(Y=3|X=2)=P(X=2;Y=3)/P(X=2)=0.1/0.35=2/7

d)

here as P(X=1;Y=1)=0.05 ; while P(X=1)*P(Y=1)=0.1*0.2=0.02

as they both are not equal ; hence X and Y are not independent,