• Fsc Part 2 Maths Ch3 Solution

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. A complete solved exercises of Fsc Part 2 mathematics book (math 12) for 12th class. The Book is same for Fsc part 2, ICS part 2, 12th class, Punjab Textbook Board of Pakistan. Student can find all solved questions with step by step guidance to understand and Built problem solving skills. Notes (Solutions) of Unit 03: Integration, Calculus and Analytic Geometry, MATHEMATICS 12 (Mathematics FSc Part 2 or HSSC-II), Punjab Text Book Board Lahore.

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. Written Notes, Video Lectures, Learn Languages and Past Papers are the requirement for every students.

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-?

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Mathematics 2nd Year All Chapter Notes Math FSc Part 2 “Class 12 Mathematics Notes” Mathematics-XII (Punjab Text Book Board, Lahore) These Mathematics-XII FSc Part 2 (2nd year) Notes are according to “Punjab Text Book Board, Lahore”. Very helpful notes for the students of 2nd year to prepare their paper of Maths according to syllabus given by Federal Board of Intermediate and Secondary Education (FBISE), Faisalabad Board, Multan Board, Sargodha Board, DG Khan Board, Gujranwala Board, Rawalpindi Board or others board of Punjab, Pakistan. These 12 Class Math Notes are obtained from mathcity.org.

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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.

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. (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.

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. 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. This is called statistical inference.

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.

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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.   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.

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The sampling distribution of the mean is the probability distribution or the relative  frequency distribution of the means X of all possible random samples of the same size that could be selected from a given population. The mean of this distribution is represented by x- and the standard deviation which is called the standard error of the (7) mean, by 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.

Fsc Part 2 Maths Ch3 Solution

Here the population consists of all the bulbs that could be produced by the process. The elements of the population are the individual electric bulbs. (2) (3) (4) (5) (6) A population containing finite or fixed number of elements is called a finite population otherwise it is infinite. Intel hd graphics driver windows 7.

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.

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. Examples (i).

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. Are not coated correctly in the most of the cases.

A population which consists of concrete objects is called an existent population otherwise it is called hypothetical population. A small part of a population is called a sample. Technique of selecting a true sample is called sampling. We’ll discuss sampling later.

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