Fsc Part 2 Maths Solution
FSc Part 1 Mathematics Book 1 MCQ Objective Type Questions & Answers. Inter Part 1 Mathematics Chapter 14 Solutions of Trigonometric Equations online. 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. Give examples of their sharing as it occurs in distributed systems. By George Coulouris, Jean Dollimore and Tim Kindberg. HTML is a relatively straightforward language to parse and render but it confuses presentation with the.
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.
(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.
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 . 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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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.
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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.
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.
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. 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.
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-?
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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.
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Technique of selecting a true sample is called sampling. We’ll discuss sampling later. 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-.
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.
Fsc Part 2 Maths Book Chp 1 Dailymotion
Chapter # 1 Functions and Limits.
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 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.
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. It also elaborates the formation of a function.As all the functions are not of the same type at all. This video expalins the useablity of it as well.
Fsc Part 2 Math Chapter 7 Solution
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.