1. Fbise Fsc Part 2 Maths Notes

Notes (Solutions) of Unit 03: Integration, Calculus and Analytic Geometry, MATHEMATICS 12 (Mathematics FSc Part 2 or HSSC-II), Punjab Text Book Board Lahore. It’s seriously very very disappointing to see same notes on many websites. These notes you have provided are on mathcity.com, office.com, mathstudyfirstudents.com and fsconline.com and it realizes students of course every one is just trying to earn in the name of making a platform for students instead of providing true notes and doing some effort! Sep 23, 2018  This vedio is all about the application of a function in our daily life. It also dexplains how the things can be related with each other, with examples. Mathematics MCQS Questions With Answers For Class 12 /XII Class FSC/FA Math Part- 2 Chap # 7 Boards MCQS Solved, Short & Long Questions Notes LEAVE A REPLY Cancel reply.

(ii) Systematic Sampling A sample of size n is defined to be a systematic random sample if it is obtained by choosing one unit at random from the first k units and thereafter selecting every kth unit after the N units in the population have been serially numbered from 1 to N or arranged in a systematic way. (iii) Stratified Sampling A sample of size n is defined to be stratified random sample if it is selected from a population which has been divided into a number of non-overlapping groups called strata, such that parts of the sample is drawn at random from each stratum. (iv) Cluster Sampling A random sample is said to be a cluster sample if it consists of first selecting at random groups of individual units, called cluster into which a population can be divided and then including in the sample either all the units from each of the chosen clusters, or selecting a random sample of the units which the cluster comprises. Muhammad Na eem Sa ndhu, Assist ant Professor, Department of Mathematics, University o f Engineering and Technology, Lahore 05: Sampling Distributions and Methods of Estimation (4) Sampling Distribution A frequency distribution of all the means of the samples is called the sampling distribution of the mean. Explanation: Suppose we draw samples from a normally distributed population with mean 100 and a standard deviation of 25. We draw samples of 5 items each and calculate their mean.

Notes (Solutions) of Calculus and Analytic Geometry, MATHEMATICS 12 (Mathematics FSc Part 2 or HSSC-II), Punjab Text Book Board Lahore. There are seven units in this book and we have work hard to make easy and suitable solutions for students and teachers so that it help them learn things quickly and easily. Please click on a desire unit to view the solution of any particular exercise. This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License or stated otherwise. To view PDF files, there must be PDF Reader (Viewer) installed on your PC or mobile or smartphone.

Simple random sampling, stratified sampling, systematic sampling, cluster sampling etc. Non-probability Sampling a non-probability sampling is a process in which the personal judgment determines which units of the population are selected for the sample. It is also called non-random or judgment sampling Muhammad Na eem Sa ndhu, Assist ant Professor, Department of Mathematics, University o f Engineering and Technology, Lahore 05: Sampling Distributions and Methods of Estimation (3) Types of Sa mpli ng Random or Probability Sampling Non-random or Judgment Sampling In probability sampling or random sampling, all the items in the population have a chance of being chosen in the sample. In judgment sampling, personal knowledge and opinion are used to identify the items from the population that are to be included in the sample.

Sometimes judgment sample is used as pilot or trial sample to decide how to take a random sample later. The rigorous statistical analysis can be done only with the probability samples.

This is called statistical inference. The distribution of a statistic is called a sampling distribution. The sampling distribution helps us understand how close a statistic to its corresponding population parameter is. Typical parameters of interest include:  Mean  Proportion Variance The standard statistic that is used to infer about the population mean is the sample mean.  Definitions: (1) A population is defined as an aggregate of all individuals, or elements, or objects under consideration. They are called statistical units.

Numerical information or values drawn from sample are called statistic. It varies from  sample to sample from the same population. For example sample mean X and sample standard deviation S. The difference between parameter and statistic due to small sample is called sampling error. It can be reduced by increasing the sample size to a sufficient level.  sampling error = X   The non sampling errors are those which arise due to defective sampling frame or information not being provided correctly. For example, income, sale, production age etc.

05: Sampling Distributions and Methods of Estimation (1) 05. Sampling and Sampling Distributions We are often interested in calculating some properties (called as the parameters) of a population.

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Dear Students, This section contains Written Notes for Mathematics Subject for 11th / FA / F.SC – I. All the notes are as per the syllabus of Federal Board of Intermediate and Secondary Education, Islamabad. This section will really be helpful for the students of the class 11th / FA / F.SC – I. The students can download all of these notes on Mathematics for free from this Section. The Notes are designed in such a way that you people will definitely score very good percentage in your Exams. I am requesting you all to please share this knowledge with every student and every individual who wanted to learn something because sharing is caring. So, share it with the people you really care.

You Can Easily View or Download These Notes For PC. To view PDF files, there must be PDF Reader (Viewer) installed on your computer. To Download PDF Viewer and other Softwares. Chapter # 1 Functions and Limits.

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Fbise Fsc Part 2 Maths Notes

For a very large population, the exact calculation of a parameter is typically prohibitive. A more economical and sensible approach is to take a random sample from the population of interest, calculate a statistic related to the parameter of interest, and then make an inference bout the parameter based on the value of the statistic.

Relationship between the population distribution and sampling distribution of the mean for a normal population is: Suppose we increase our sample size from 5 to 20. This would increase the effect of averaging in each sample and would expect even less dispersion among the sample means Examples (1) Consider the data concerning the experience of five motorcycle owners with life of tires. Owners Carl Debbie Elizabeth Frank George Total Tire Life 3 3 7 9 14 36 (in months) Because only five people are involved, the population is too small to be approximated by a normal distribution. We will take all of the possible samples of the owners in groups of three.  Compute the sample mean X, list them and compute the mean of the sampling distribution x-?

Sampling is said to be with replacement if the selected unit is replaced to the population before selecting the next unit. Thus sampling unit can be selected more than once. Case (i) when sampling is without replacement from a finite population: x- =  and x- =  n N-n N-1 Muhammad Na eem Sa ndhu, Assist ant Professor, Department of Mathematics, University o f Engineering and Technology, Lahore 05: Sampling Distributions and Methods of Estimation where N-n N-1 is (2) called the ‘finite population multiplier’ or ‘the finite population correction n is less than 0.05, then finite population multiplier need not be N used. For a large N, this factor, of course, approach 1 and hence can be ignored. The usual rule of thumb is to consider N is large enough if it is at least 20 times larger than n. Case (ii) when the sampling is with replacement from infinite population:  x- =  and x- = n (8) An element of a sample is called a sample unit.

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Examples (i). The manager of an automobile agency is interested in fuel economy of the Suzuki cars in the company’s fleet. Here the population consists of all Suzuki cars in the fleet. The elements of the population are the individual cars. A quality assurance manager wishes information about the quality level of the firm’s for manufacturing light bulbs. Here the population consists of all the bulbs that could be produced by the process.

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  Types of Random Sa mpli ng (i) Simple Random Sampling Goldfish Bowl Procedure: In this procedure each unit of the population is allotted a different serial number from 1 to N and record each number on a card or on a slip of paper. Place these numbered cards or the folded slips of paper in a bowl or a basket and mix them thoroughly. Then draw out blindly the desired number of cards or the folded slips of paper one by one for the sample. Using a Random Number Table: Assign a number from 1 to N to each of the N units in the population. Consult a random number table, read digits in groups of two or three or more according to the largest number assigned to a unit in the population, from the table vertically, horizontally or diagonally.

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A population in which every sampling unit have similar characteristic and have equal chances of selection in sample is called a homogeneous population. Definition (Sampling) Sampling techniques are used to estimate the population parameters on the basis of samples measures called as statistic and usually these inferences are mean, variance, standard deviation, Skewness and Kurtosis etc. That’s why we discuss here sampling distributions as an application of these inferences. Sampling methods (1) Probability Sampling (2) when each unit in population has known non-zero (not necessarily equal) probability of its being included in the sample, the sampling is said to be probability sampling is also called random sampling.

It’s seriously very very disappointing to see same notes on many websites. These notes you have provided are on mathcity.com, office.com, mathstudyfirstudents.com and fsconline.com and it realizes students of course every one is just trying to earn in the name of making a platform for students instead of providing true notes and doing some effort! I mean what is the reason then left?

Are not coated correctly in the most of the cases. Bias is a cumulative component of error which arise due to defective selection of the sample or negligence of the investigator. Errors due to bias increase with an increase in the size of the sample.

A complete list of all possible sampling factor’. If the sampling fraction (9) (10) (11) (12) (13) (14) units is called a sampling Numerical information or frame. Values drawn from population are called parameter. For example population mean  and the standard deviation .