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Technical articles with clear explanations and examples
Differential Equations
Introduction We need to develop various mathematical models to establish relationships between multiple variables in real life. In this direction, differential equations play an important role. These are applied parts of mathematics and used in calculus. In this tutorial, we will discuss the meaning, order, degree, and types of differential equations with solved examples. Differential Equations Differential equations are mathematical statements containing functions and their derivatives. It describes the relationship between the variables with their rate of change. It is used in engineering, science, biology, finance, etc. The differential equations contain at least one ordinary derivative or partial derivative term. ...
Read MoreFundamental principle of counting
Introduction You go shopping on a bright sunny day. You chose nice jeans and decided to pay with a credit card. But suddenly you realized that you couldn't remember your PIN. What a tragedy! Now what you can think of is to list all possible combinations to understand your pin. How many combinations are possible? If you list and count all possible combinations, the answer to this question will be difficult. In these situations, the basic principle of counting or the principle of multiplication is useful. Number system A number system is defined as a system of writing to ...
Read MorePoisson Distribution
Introduction Poisson distributions are frequently used to comprehend various events that take place continuously over a predetermined period of time. The Poisson distribution is a discrete function , therefore the variable can only take values from a list of (possibly infinite) numbers. The Poisson distribution is used in probability and statistics concepts of mathematics. It is a discrete probability distribution used in probability theory and statistics to express the chances of happening that a given number of events will happen within a given time period and regardless of the amount of time that has passed since the last outcome. Definition ...
Read MoreRandom Sampling
Introduction Sampling techniques refer to the different sampling techniques used to collect different types of samples in statistics. If you need to make statistical inferences about a population, it is almost impossible to collect data from all the units that belong to that group. In these situations, various sampling methods can help you select the correct sample from this population for analysis. In this tutorial, we will discuss random sampling, its type, formulas, and examples. Random sampling Definition Random sampling can be considered as a case of probability sampling. where each and every unit from the population into the ...
Read MoreRemainder
Introduction Division is the basic arithmetical operation in mathematics. It is the process of distributing things into equal parts. When the dividend is not completely divisible by the divisor it left a number or the value is known as the remainder. In mathematics, in numerous instances, the leftover part or value is known as residues. Sometimes in many calculations residues are neglected or round off to obtain the answer in the whole number. For example, in the decimal number 5.04, the number after the decimal is 4. It represents remainder or residue. Sometimes to give only a whole number answer, ...
Read MoreSampling Error
Introduction In any business or research activity, a large number of data is produced, which becomes difficult to analyse. In this direction, a statistical process, sampling, is useful to analyse the entire population. However, in doing so, some error arises due to various reasons. For accurate data analysis, one must know about sampling and the various types of error associated with it. In this tutorial, we will discuss sampling, sampling errors, a basic formula, properties, and ways to minimize sampling error with solved examples. Sampling In statistics, sampling is defined as the process of selection of specific data from a ...
Read MoreProgram to find the sum of series 1*2*3 + 2*3*4+ 3*4*5 + . . . + n*(n+1)*(n+2)
The sum of the series is the value of all terms in the given series added together in a particular pattern. Here given pattern is in the form of the: ∑ (n*(n+1)*(n+2)) as (n*(n+1)*(n+2)) is the last term in the given pattern. The following article discusses 3 approaches in detail to find the given sum of the series with different time and space complexities. Problem Statement Now, let us see how to calculate the sum of series 1*2*3 + 2*3*4 + 3*4*5 + . . . + n*(n+1)*(n+2). Sample Examples Let’s try to understand this problem with the help ...
Read MoreCount of substrings with the frequency of at most one character as Odd
Substrings are the subsets or sequences of contiguous characters of a string. Now, in this problem, we need to find the number of substrings with the frequency of at most one character as odd. Let us see how we should proceed to solve this problem. Let’s try to understand this problem with the help of some examples. Input s = “ksjssjkk” Output 21 Explanation − As the frequency of the characters in the given string is given below− k → 3 s → 3 j → 2 Now, substrings with ...
Read MoreFind the next number by adding natural numbers in order on alternating indices from last
A numerical string is used to store a value of a number if we want to store a huge valued integer. As we know, we can not store a number greater than 32 bits in the computer with its datatype as int. So to avoid the overflowing condition, in this problem, we will take a numerical string as our input rather than an int variable so that we can work this problem on a larger scale of numbers. Problem Statement Now, in this problem, we need to find the following number by adding natural numbers in order on alternating indices ...
Read MoreMaximize the String value by assigning values in the range [1, 26] to each character
There are 26 total different alphabets exist in the English language. If we want to change the alphabet characters into numerical values then we need to assign the alphabet, values between 1 to 26 only. Now, in this problem, we need to Maximize the String value by assigning values in the range [1, 26] to each character. Let us see how we should proceed to solve this problem. Let’s try to understand this problem with the help of some examples. Input s = “blpsBpPtT” Output 221 Explanation Here, in this ...
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