linear Alg-2 jobs

below attached are quiz and hw , i need both done within max 12 hrs . i need all working as well 

NOTE : 3

(

B

)

,

3(C) ,4(B),4(C),5(A),5(B) ARE WRONG . AS A PROOF I PAST

ED

THERE

Qu

e

stion 1: (3 points)
Answe

r

s to the fo

l

lowing 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.
 

Suppose that the lifetime, T, for a certain type of disk drive follows an exponential distribution.

 
(a) If it is given that 6% of drives fail within

2

years, find the parameter λ for the exponential distribution.
 _____

5.5466

_____ 

 
(b) Find E(T).
 _____5.5466_____

 
(c) Calculate the

probability

that the lifetime T for a randomly chosen disk drive exceeds 0.

9

years.
 _____3.30

7

0*10^

–

7_____ 

 

 

Question 2: (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.

 
Suppose the discrete random variable

X

has the following probability distribution.
 

x

p(x)

x1

=

3

p1=0.1

x2=4

p2=0.15

x3=7

p3=0.05

x4=9

p4=0.3

x5=12

p5=0.4

 
 

(a) Find E(X).

 ____

8.75

______ 

 Explanation:

(b) Find var(X).
 ____

11.0875

______ 

Question 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

+

80

Y
 

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

_____ 

 
(c) Find the probability that the total cost of service, for a randomly chosen car, will be no more than $350.00.
 _____0.9370_____ 

 

Probability =

Question 4: (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.
 

Suppose that the diameters of particles in a sediment are distributed uniformly between 0.5 and 2.1 mm. Let D be the diameter of randomly chosen particle.

 

(a) Find E(D).

 ______

1.3

______ 

 
(b) Find the standard deviation sd(D).
 _____0_____ 
 0 since uniformly distributed

(c) Find the proportion of particles with diameters between 0.6 and 0.9 mm.
 ____

0.0900

______ 

Probability =

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______ 

 

(b) What is the value of the correlation coefficient ρX,Z?
 _____

0.3780

_____ 

(
)
9
5.5466
7
5.5466

9!

3.307010

e
–
–
=

=´

(
)
(
)
(
)
(
)
(
)
(
)

30.140.1570.0590.3120.4

8.75

EX

=+

+++

=
(
)
(
)
(
)
(
)
(
)
(
)

22222

var0.138.750.1548.750.0578.750.398.750.4

128.75

11.0875
X

=-

+-+-+-+-

=
(
)
(
)
(
)
(
)
80

120802.6

328

ECEXEY

=+
=+
=
(
)
(
)
(
)
(
)

[

]

[
]
[
]
(
)
(
)

varvar80

var80var28080

20280.52

206.16

ZXY

XYEXYEXEY

=+

=++-

=+
=
(
)

~328,206.16

CN

(
)

3500.9370

PZ

<=

(
)

0.52.1

1.3
2
ED
+

==

(
)
(
)

Pr0.9Pr0.6

ZZ

£-£

0.8160.726

0.0900
=-
=
(
)
(
)
(
)
(
)

cov,

varvarvar

7

XZ

XZXZ

=+-+

=
(
)
(
)
(
)
(
)
cov,
,
7
7
0.3780
XZ
XZ

stdXstdZ

r
=
=
=
2

0.06

2!

5.5466
e
l
l
l
–
=

Þ=

(
)

ET

l
=
9
9!
e
probability
l
l
–
=