Math Answers

Find the variance of a discrete random variable X - the number of occurrences of event A in four independent tests, if the probability of occurrence of event A in each test is 0.1. Write in the form of a table the law of distribution of the random variable X

A Kelifa Business Centre plans to sell two models of an item at costs of $350 and $400. The $350 model yields a profit of $85 and the $400 model yields a profit of $90. The total demand per month for the two models will not exceed 150. Find the number of units of each model that should be stocked each month in order to maximize the profit. Assume the merchant can invest no more than $56,000 for inventory of these items.

Formulate Linear Programming problems (LPP)

Find the optimal solution by Graphic method

Draw all possible sample of size 2 from the set A={2,3,4,6,8} with replacement and find their mean values. Now construct a frequency distribution of these mean values. then find the mean of this frequency distribution. then finally verify that this mean is equal to the mean of the set A.

Assume that the length of a phone call (minutes) is a continuous random variable X with probability density function {f(x)=1/10e^-0.1x} . If someone arrives at a phone booth just before you arrive, find the probability that you have to visit

1). Less the 5 minutes

2). Greater than 5 minutes

3). Between 5 and 20 minutes

A lot of 12 Compresser tanks is checked to see whether there are any defective tanks. three thanks are checked for leaks. if 1 or more of the 3 is defective, the lot is rejected. Find the probability that the lot will be rejected if three are actually 3 defective thanks in the lot.

If F(x) be the distribution function of a random variable X, then F(infinity) is equal to

A school organized a book fair and in this book fair a book seller is selling his books under the following rules:

There are three different packages available.

First package contains 2 Islamic books, 2 Science books and 2 Geography books, second package contains 2 Islamic books, 4 Science books and 1 Geography books and third package contains 3 Islamic books, 4 Science books and 5 Geography books. The book fair has a total of 250 Islamic books, 300 Science books, and 270 Geography books. First package makes a profit of Rs. 120, second package makes Rs.100 and third package makes Rs.270 per pack. 

How many packs should be made to maximize book fair profits?

What will the profit be?

Brute Force Algorithms

A club with 10 students elects a president, vice president, treasurer, and secretary. No student can hold more than one position. How many ways are there to select the class officers?

A school organized a book fair and in this book fair a book seller is selling his books under the following rules:

There are three different packages available.

First package contains 2 Islamic books, 2 Science books and 2 Geography books, second package contains 2 Islamic books, 4 Science books and 1 Geography books and third package contains 3 Islamic books, 4 Science books and 5 Geography books. The book fair has a total of 250 Islamic books, 300 Science books, and 270 Geography books. First package makes a profit of Rs. 120, second package makes Rs.100 and third package makes Rs.270 per pack.

How many packs should be made to maximize book fair profits?

What will the profit be?

Define and give examples of injective surjective and bijective functions. Check the injectivity and surjectivity of the following function f: NN given by f(x)=x2