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1.    Two fair cubes are rolled. The random variable X represents the difference between the values of the two cubes.

a)    Find the mean of this probability distribution. (i.e. Find E[X])

b)    Find the variance and standard deviation of this probability distribution.

(i.e. Find V[X] and SD[X])

The random variables A and B are defined as follows:

A = X-10 and B = [(1/2) X]-5

c) Show that E[A] and E[B].

d) Find V[A] and V[B].

e) Arnold and Brian play a game using two fair cubes. The cubes are rolled, and Arnold records his score using the random variable A and Brian uses the random variable B. They repeat this for a large number of times and compare their scores. Comment on any likely differences or similarities of their scores.

● Courier Management

The main aim of the Courier Management Mini DBMS project is to deliver the parcel. We aim to demonstrate the use of create, read, update and delete MySQL operations through this project. The project starts by adding details of the courier branch and staff working in their respective branches. The staff then adds sender and receiver details of that parcel i,e. Booking details. Then, the parcel is scheduled for delivery. Now, when the parcel is received by the receiver branch, they deliver the parcel and delivery status is shown

Choose one device that you own and use - a laptop, tablet or smartphone.

Calculate the total costs of ownership (TCO) for the selected device including:

Purchasing costs or software subscription fee

Operating costs (hours spent on managing IT, e.g. upgrades, fixes, troubleshooting, searching for new software, learning with new programs, providing IT support to others)

Downtime costs (lost hours due to inoperable or inaccessible computer, internet connection, viruses, etc.)

When convering amount of time to money, consider average hourly gross wage 200 CZK (around 7 EUR).

Calculate overall TCO and annual TCO.

Convert the following function to a phase representation F(t)=alpha + beta1*cos(omega*t)+beta2*sin(omega*t)

Construct the network who's activity and the relationship

Activity:A,D,E can start simultaneously

Activity:B,C>A;G,F>D,C;H>E,F

How to draw a network diagram in mathematical foundations of computer science

Prove that the following statements are true by means of mathematical induction n X

(a) ∀n ≥ 1, i=1 i(i!) = (n + 1)! − 1.

(b) 7n −2n is divisible by 5, ∀n ≥ 0.

(c) n! > n2, ∀n ≥ 4.

.Using 8’s complement arithmetic compute the value of 6278-6758 and write your final answer in decimal