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MGT301 Assignment Solution

Question No. 1 Solved

DHL should improve there service to compete the FedEx services. In this regard DHL should adopt some methods of promotions. i.e.

• Advertising
• Sales promotion
• Personal selling
• Direct mail
• Internet marketing

And they should increase there time limit because time is very important factor in business.

Question No. 2 Solved

The FedEx will compromise on their status and will give any packages to the firm then by using this they will retained their competitive edge.

IT430 Assignment

When a person want to buy any thing from an online shop and want to pay through electronic check he uses the electronic check book device. By using electronic check books he filled all the information regarding amount, date etc. and his digital signature through his private key and generates a blank electronic check.  A certificate issued by the payer bank authenticating public key of the payer is also attached with the electronic check. This blank check is sent through secure envelop which is created by encrypts his information with a symmetric key. The payee firstly decrypts the secure envelop by symmetric key and then decrypts all the information available on electronic check. The payee use a hardware device to forward the check to payers bank in secure envelop.

The reason of security of electronic checks are Digital signature and Public key cryptography use one for encrypt and other for decrypts.

STA301 Assignment No. 3......Solution

Question 1:

1. Flows in a certain type of drapery material appear on the average of three in 250 square feet. If we assume the poison distribution, fin the probability of at most one flow in 450 Square feet.

P(X = x) = e^-2 2^x                                       x = 0, 1, 2, 3, 4…..

                     x!

Answer:

Sign of at most is (≤)

So,

We have to find:

As he said (One flaw in 450)

So (x=1)

Now

P(x ≤ 1) = e^-5.4 (5.4)¹

                        1

              = (o.oo4) (5.4)

                          1

P(x ≤ 1) = 0.0216

[ùe^-5.4 =          1             = 0.004 ] (See Example on page # 217)

                (2.71828) ^-5.4

2. What is the mean and variance for the given poison distribution of a random variable X;

Answer:

X	X2
0	0
1	1
2	4
3	9
4	16
X=10	X2 = 30

Mean = X/n

            = 10/5

            = 2

So, Mean is 2

Now find variance

E(X) = μ
E(X) = 2 
V(X) = σ2 = μ
V(X) = σ2 = 2

Question 2:

              I.      For the following probability distribution;

Show that E (5x + 3) = 5E(x) + 3

X	P(X)
0	0.3
1	0.6
2	0.1

Answer: (see page 178)

X	P(X)	XP(x)
0	0.3	0
1	0.6	0.6
2	0.1	0.2
	P(x) = 1	XP(x) = 0.8

µ= E(X) = Xp(x) = 0.8

So

5(EX) + 3

5(0.8) + 3

4+3 = 7

Hence Prove that,

E (5x + 3) = 5E(x) + 3 are equal

B) Find the distribution function for the following density function.

F(x) = 1/8x               0 ≤ x ≤ 4

Answer: ( see lect 25 )

P [0 ≤ x ≤ 4] = 4f0 f(x) dx

                    = 4f0 2x dx

                    = 2 [x²/2]

                    = [4²]

                    = 16

Question 3:

(See & read page # 189 for joint probability distribution)

Let X & Y have the joint probability distribution described as follows,

X	1	2	3
Y
1	1/12	1/6	0
2	0	1/9	1/5
3	1/18	¼	2/15

Find the two marginal probability distribution for X and Y.

Answer:

X	1	2	3	P(X = xi) G(x)
Y
1	1/12 = 0.08	1/6 = 0.17	0	0.25
2	0	1/9 = 0.11	1/5 = 0.2	0.31
3	1/18 = 0.06	¼ = 0.25	2/15 = 0.13	0.44
P(Y = yj)	0.14	0.53	0.33	1

Marginal Probability Distribution for X & Y

So

F(x, y) = P (X = x_i and Y = y_j)

            = P (X = x_i) (Y = y_j)

           = 1. 1

           = g(x) h(y) = 1

An idot in a Class room

"If there are any idiots in the room, will they please stand up" said the sarcastic lecturer.

After a long silence, one freshman rose to his feet. "Now then mister, why do you consider yourself an idiot?" enquired the lecturer with a sneer.

"Well, actually I don't," said the student, "but I hate to see you standing up there all by yourself."