write up
strength
Q3b-3c-5b.docxQuestion 3: (3 points)
Answers to the following questions should be calculated in Matlab and given to 4 decimal places. Be careful not to introduce errors by rounding in any intermediate calculations as this may lead to an incorrect final answer.
In a certain workshop, the total cost, C for servicing a car is
C=X+80Y
where X is the cost of parts and Y is the time (in hours) taken to perform the service. Suppose, for a randomly chosen car, that
X∼N(120,202) and Y∼N(2.6,0.52) independently.
(a) Find E(C).
_____328_____
(b) Find var(C).
_____206.16_____
THE ABOVE WAS WRONG SO I TRIED BELOW TWO ANSWERS AS WELL AND THEY TOO WERE WRONG
3(b) Var(Z) = Var(X) + 80*80*Var(Y) =202+80*80*0.52 =3530 ----------------------------------------------WRONG
3b) 42534.56 ------------------------------------------- WRONG
(c) Find the probability that the total cost of service, for a randomly chosen car, will be no more than $350.00.
THE ABOVE WAS WRONG SO I TRIED BELOW TWO ANSWERS AS WELL AND THEY TOO WERE WRONG
3(c) P( X < 50 ) = P ( Z < (350-120)/202 ) =P( Z < 1.1386) = 0.8726 ------------------------------------------------- WRONG
3c) 0.5425------------------------------------------------- WRONG
Question 5: (2 points)
Answers to the following questions should be calculated in Matlab and given to 4 decimal places. Be careful not to introduce errors by rounding in any intermediate calculations as this may lead to an incorrect final answer.
Let X and Y be independent random variables with variances 7 and 1 respectively and let Z=X+Y.
(a) What is the value of cov(X,Z)?
______2.6457______
5(a) cov(X,Z) = E( X-E(X))(Z-E(Z)) = E( X-E(X))(X+Y-E(X+Y)) = E( X-E(X))(X-E(X))- E( X-E(X))(Y-E(Y)) = V(X)- COV(XY) = 7 -----------------------------------------------------------CORRECT
(b) What is the value of the correlation coefficient ρX,Z?
_____0.3780_____
THE ABOVE WAS WRONG SO I TRIED BELOW TWO ANSWERS AS WELL AND THEY TOO WERE WRONG
5(b) ?_XZ=(COV(X,Z))/(SD(X)SD(Z)) Var(Z) =VAR(X+Y)=VAR(X)+VAR(Y) =7+1 = 8 ?_XZ=7/(v7 v8) =v(7/8) = 0.9354 -------------------------------------------- WRONG
(
)
~328,206.16
CN
(
)
3500.9370
PZ
<=
(
)
(
)
(
)
(
)
cov,
,
7
7
0.3780
XZ
XZ
stdXstdZ
r
=
=
=
(
)
(
)
(
)
(
)
80
120802.6
328
ECEXEY
=+
=+
=
(
)
(
)
(
)
(
)
[
]
[
]
[
]
(
)
(
)
varvar80
var80var28080
20280.52
206.16
ZXY
XYEXYEXEY
=+
=++-
=+
=
