Question

An Instructor has given a shot quiz cosisting of two parts For a randocmly selected student, let X-the number of points eamed on the frst part and Y-the number of points earsed on the second pa, Suppose that the joint pmf of X and Y is givon in the accompanying table обк, у) 10 15 o03 0.06 002 0.10 0 0.04 0.17 020 0.10 10 0.01 0.15 0.11 0.0 5 (Eter your answor to one decimal place) (a) the scoe recorded in the grade book is the sotal munber of points eamed on the two parts, whot is the expected recorded score E(X Y (b) the maximam of the two scores is recorded, what is the expected recerded score? (Enter your answer to two decimal places Need Help? Telk to a Tuter Raad Wch Ask Your Teacher My Notes 2. -/1 peints DevoreStat9 5.E.026 Comider a semall ferry that can accommodate cars and bunes. The toll for cars is $3, and the toll for buses is $10 Let X and Y deote the umber of crs and buses, respectively, caried ona single brip. Suppose the joint distribuion cf X and Y is as given in the tsble below plx) 1 0.010 0.025 0.015 0.020 0.050 0.030 0.075 0.050 2 0,075 0.150 0.00 0.060 0.000 3 0.040 4 0.100 0.000 0,030 0.070 Compute the expected revenue from a sinole trip (Round your awer to two decimal places)

Answer 1

1)

	y
x	0	5	10	15	Total
0	0.03	0.06	0.02	0.1	0.21
5	0.04	0.17	0.2	0.1	0.51
10	0.01	0.15	0.11	0.01	0.28
Total	0.08	0.38	0.33	0.21	1.00

marginal distribution of x:
x	P(x)	xP(x)	x^2P(x)
0	0.210	0.000	0.000
5	0.510	2.550	12.750
10	0.280	2.800	28.000
total	1.000	5.350	40.750
E(x)	=		5.3500
E(x^2)	=		40.7500
Var(x)=	E(x^2)-(E(x))^2=		12.1275

marginal distribution of y:
y	P(y)	yP(y)	y^2P(y)
0	0.080	0.000	0.000
5	0.380	1.900	9.500
10	0.330	3.300	33.000
15	0.210	3.150	47.250
total	1.000	8.350	89.750
E(y)	=		8.3500
E(y^2)	=		89.7500
Var(y)=σy=	E(y^2)-(E(y))^2=		20.0275

E(XY) =∑xyP(x,y)=41.75

a)

Covar(y,x)=E(XY)-E(X)*E(Y)=

-2.92

b)

Correlation coefficient ρ=Cov(X,Y)/√(σx*σy)=

-0.19

2)

E(X)=∑xP(x)=		2.95
E(Y)=∑yP(y)=		0.8

expected revenue =3*2.95+10*0.8 =16.85