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# PROBABILITY AND STATISTICS S CHAND PDF

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PDF | Linear correlation coefficient Linear regression; Non-linear Text Book: Probability and Statistics By T K V Iyengar S chand, 3 rd Edition. PROBABILITY AND STATISTICS: (FOR 2ND YEAR wildlifeprotection.info STUDENTS OF JNTU, ANANTAPUR). Dr. T K V Iyengar, Dr. M.V.S.S.N. PRASAD, S. Aim: To acquire basic knowledge in concepts of probability and statistics. Objective: The Edition, Sultan Chand & Sons educational Publishers. 2. Dr. B.S.

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damentals of probability and statistics using mostly calculus. I have given . For an event A of a discrete sample space S, the probability of A can be computed. You may go to the website Library Genesis and search for the book. If not found, search by the name of the book. You will find a list of books relevant to the topic. Fundamentals of Mathematical Statistics By S.C. Gupta – PDF Free Download Publisher: Sultan Chand & Sons; Language: English; ISBN

Popular Files. January June 2. Ixi -A I I. A creates artificiality and. Xi-X'P I. For the frequency distribution Xi If. Taking into COnSideration the pros and cons and also the wide applications of standard deviation in statistical theory. The square of standard deviation is called the variance and is given by.

It lIlay also be pointed out that standard deviittion gives greater weight to extreme values and as such has not found favour with economists or businessmen who are more interested in Hie results of the modal class'.

X overcomes the drawback of ignoring the signs in mean deviation.. Moreover of all the measures.. The same result could be obtained altematively as follows: Mean square deviation is given by. Different J'ormulae For Calculating Variance. Thus s. By definition. Measures or Dispersion. A' Obviously s: We have 0'.

By definition.. But 'J.. Relation between 0 and s.. Generally the poin. If the values ofx and f are larg. In order to overcome this difficulty. S out to be in fractions. In that. If we take d. Then We have to prove that.. We know that the mean of a series in A. Find the mean deviation from tire mean ant! Hence the result. Prove that for any discrete distribution standard deviation is not less than mean deviation from mean.

Let Xi If. Let Xi If.: Skewness and Kurtosis e r. Ii Xi. Hence Neglecting x. Also l: We bave l. Mneglecting higher powers. For a group of candidates. Find the corrected mean and standard deviation corresponding to tlte corrected figures. Measures of Dispersio! Corrected mean..

Skewness and.. IM 3 and bigber powers of x. Let then XI i. Ie mean oJ t Ie comb' med series. X2 the means. Variance of the combined series. Skewness and Kurtosis I x2i. Substituting from 3' lOb and 3'10c in 3' Xi and OJ. We have. A -'8 1. The series having greater C. Whenever we want to compare the variability of tht WO series which differ widely in their averages or which are measured in different units.

Co-efficient of Variation. Based upon mean deviation: Average from whkh it is calculated Based'upon standard deviation: Co-efficient of Dispersion. Based upon qua nile deviation: For comparing the variability 01 two series. IX6 Total waces paid AH: Sinl'e C. Iii a The average monthly wages l. Measures' of Dlspersiob. OI O No. OQ FirmA Firm B N. In u'IIiill Jirm.

The combined variancc 0: Clllicut Unlv. Prove that the mean deviation about the mean frequency of whose ith size Xj is It is given by Number 9 16 12 26 14 12 6 5 x of the variate x.

April b Compute quartile deviatIOn graphically for the following data: Marks Classes Frequency Less than 20 30 20 Jive and absolute measures of dispersion and describe the merits and demerits of standard deviation. Baroda U. Calculate the mean and standard deviation of the following distribution: Of the 10 figures.

Explain clearly the ideas impJied in using arbitrary working orgin. The arithmetic mean and variance of a set of 10 figures are known to be 17 and 33 respectively. Standard Deviation 0. What is standard deviation? Explain its superiority over other measures of dispersion.

OJ the wrong item is omitted. Calculate the mean and standard deviation if '. Mean dev. Golfer B is more. It three of the five observation are 1. Golfer A: The sum and 'sum of squares corresponding to length X in' ems. In which firm A or B. Calculate the. Team B: Firm A Firm 1J No. Which model shows more uniformity? Standard deviation. Z 1 i Which firm. Of all tJie workers 'in the two firms. A and B belonging to the same 'industry. Combined mean.

A collar manufacturer is considering the production of a new style collar to attract young men.

## NCERT Solutions Class-wise

Obtain the mean and standa: Obtain the mean and standard deviation of the sample of size obtained by combining the two samples. In a certain test for which the pass marks is Combined S. Nagpur Univ. If i is the mean value of all the measurements.

In a series of measuremen The corresponding figures for girls including the 10 failed were 35 and 9. If the deviations are small compared with the value of the mean. Find the mean deviation and variance.. Deihl Unlv. If the mean and standard deviation of a variable x m and CJ respectively.

Wiothout quetioning the propriety of this argument. In a frequency distribution. I Ina. Find the mean and variance of first n-natural numbers. Measures of Dispersion.. G2 II M. M is very small in comparison with mean M and X. Deihi Univ. G M where G is the geometric JAean of the v I MecI. G2 t '3"!

Froln' a. I'M '2 and hig. Se Stat The rth moment of a variable about the rt1ean given by I 1. We know that if d.!. Relation between"moments about mean in terms of moments about any point and vice verso. Sheppard's Corrections for Moments.. In particular. I I uY - Thus the rth moment of the variable x about mean is h r times the rth moment of the variable II about its mean. Sheppard proved that if i the frequency distribution is continuous.

But since the assumption is not in general true. Skewness and Kurtosis wherex. In case of grouped frequency distribution. Karl Pearson defined the following four coefficients. Factorial moment of order r about the origin of the frequency distribution X..

Alpha ex coefficient is used.. Factorial Moments. Alpha coefficients are defined as: The following identitfes 'ift.. Charlier's Checks. Moments about mean: Ror the frequency distribution XI if. In the usual notations. The 11h absolute moment of the variable about the 1lean -N'I. PI lind f3!. Absolute Moments. Moments about the point x 2. Comment upon tlte nature 'of distribution. Obtain tlte first four moments abom the orgin. J4 Comments of. Nature of distribution: O Dividing throughout by N and using reiatiOll 1.

If for a random variable x. Establish the relationship between the moments about mean.

## Text books 1 tkv iyengar b krishna gandhi and others

Obtain as far as possible. The first three moments of a distribution about the value 2 of the variable arc I. II and 15 respectively.. The first four moments of distribution. What are Sheppard's corrections to the central moments? Find the first four moments about tlie origin. What is the effect of change of origin and s.

Obtain mean. Show that the mean is 3. The first four moments of a distribution about. If Xi If. Mean approx. III 0 because distribution is symmetrical. Delhi Univ. What must be the value of the fourth moment about the mean in order that the distribution be i leptokurtic. If It is the magnitude of the class interval. Calculate the l'orrect frequency constants. Correct Mean:. It was. In calculating tbe moments of a frequency distribution based on observations. CC of correct values 62 al.

Required adjustement. OiJ1ainthe correct va lue of the first Jour centra I moments. These are the absolute measures of. M 0 moderately asymmetrical distribution. BangaIore Uhiv. X moments of aU order exist. As in dispersion. Measures of Skewness. Mtf - Md. If mode is iII-defined.

LimitsIor Bowley's Coefficieitt of Skewness.. I When the.. Clqss i. If Q3 Md' L if Q3 Moreover skewness is positive if: Prof Bowle3'!

We also knQw that Q3"" M d and Md. It may even happen that one of them gives positive skewness while the other gives negative skewness. Bowley's coefficient of'skewness ranges from. QI are both non-negative. It should be clearly understood that the r values of Jhe coefficients of skewness obtained by Bowley's formula and Pearson's formula are not comparable.. In these situations Pearson's cQefl'icient of s.

In practice. Nleasurt'S of Dispersion.. In BowleY's coefficienl of skewness the disturbing factor of "va riation is eliininated by divi iing the absolute measur'!

Based upon moments. The co-efficient. Md Md. The skewness is positive if the larger tail of the distribution lies towards 6 P. We observe in 3'27 and 3. Ql by the me. Negatively Skewed Distribution. Explain the methods of measuring skewness and kunosiS' of a frequency distribution.. Show that for any frequency distribution: Band Care svmmetrical about the mean om' and have the same range. If we know the measures of central tendency.

Cun'e o the type 'C' which. Karl Pearson calls as the 'Com'exit ' of cun'e' or Kurtosis..

Distinguish clearly. Why 10 we calculate in general. What do you understand by skewne. Compute the following: If the sum oif the upper and lower quartiles is and median is Less than 30 Less than 40 Less than 50 I.

Annual Sqles Rs. Find the mode of the distribution. Find tbe mean and mode oflbe distribution. Data were ootained for distribution of passengers. Examine tbe skewness of the c.

Detemline tbe mean. The fitst three moments about the origin 51 Kg.

Class inten'al. Morning hours Arithmetic mean Peak Hou. The first tbree moments about the origin are given by. X min II. Deihl Univ. What will be the nev mea.. Which value Of 'a' gives the minimum? Fill in the blanks: Skewness and Kurtosis For the following questions given correct answers: The sum of squares of deviaJions is least When measured from I If each item is increased by This shows that the distribution is a Symmetric.

In each oHalse. State which. The value of the fourth central moment French mathematicians. Jj are kno. Galileo Bul the flfSt fo. A deterministic model is defined as a model which stipulates' that the co. It may fail to. Fermat Ii If a light ture has' lasted for I ho.

I an e'xperimept is. The pheno. E-the potential difference. Pascal andP.. They stop playing before the game is completed. Liapounoff Central Limit Theorem. The person who ftrst gains a certain number of pOints wins the stake.. De"Moivre also did considerable work in this field and published his famous 'Doctrine of Chances' in Bernoulli in Markoff For example: Bayes Inverse probability.

Exhaustiye Events. Russian mathematicians also have made very valuable contribUtions to the modem theory of probability. Bernoulli whose 'Treatise on Probability' was publiShed posthwnously by his nephew N.

Chebyshev who foUnded the Russian School of Statisticians. Mises and R. II tossing of a coin there are two exhaustive cases.

The famous 'problem of points' posed by De-Mere to Pascal is: Khintchine law of Large Numbers and A. Next stalwart in this fteld was J. The experiment is known as a triafand the outcomes are known as events or casts. In this section we wiUdefane and explain the various tenns which are used in the'definition of probability. Trial and Event.

Chief contributors. How is. In addition 10 these. Independent events. Several ev. Ving of an ace is 4. If a ttial results in n exhaustive. Exhaustive number of cases n. Mutually exclusive events. Equally likely events. Since out of the above 7 possibilities. This definition of Classic8I Probability breaks down in the following cases: The following are the P Limitations of Ciassieal Definition.

Probability 'p' of the happening of an event is also known as the probability of success'and the PfObability 'q' of the non. It is asSUl7U! If a trial is' repeated.. Ossible combinatioqs for these twO 'over'days: E is called an impossible event. A king. A bag contains 3 red. Theory of Probability Example 4. Out of 6 while balls 1 ball can be drawn in tiCI ways and out of 7 blue balls 1 ball can be drawn in 7CI ways.. Show that lhe chance of drawing two aces is What is the' probability that two balls drawn are white and blue?

Find tMprobability that i all are diamond.. Find the chance that they are a king. A pack of cards contains 4 kings. Assuming t! What is the probability of getting 9 cards of the same suit in one hand at a game of bridge?

One hand in a game of bridge consists of 13 cards. Find the chance that i it is a multiple of5 or Since there are 4 suits in a pack of cards. Find the probability offoT1ning. P [Committee has no purchase officer] In order that the committee has no purchase officer. Hence ii P [ Committee has no purcha:. The chartered accountant must be in the committee. It should have at least one from the purchase department.

A committee of 4 people is to be appointed from J officers of the production department. Since the number 21 is common ill both the cases. P [ Committee has at least one purch. M are 11!

## All time popular Study Materials

Following are the 8 possible combinations of 4-S's coming consecutively: P and I offourth kind viz. Each coefficient in the equation td. The two letters Rand E can occupy llp2. The number of ways in which there will be exactly 4 letters between Rand E are enumerated below: We know that the product of two positive quantities whose sum is cQnstant is greatest when the quantities are equal. Theory of Probability 49 Solution. The sum of two non-negative quantities is equal to 2n.

Acquire Knowledge in a Tools and concepts of Micro Economics. Develop skills in providing solutions for a Managerial decisions of an organization. Develop effective communication in Business and Accounting transactions.

Ascertain the profitability and soundness of the organization. UNIT — I: Demand Analysis: Determinants of demand — demand function - law of demand and its exceptions - elasticity of demand — types - measurement and significance of elasticity of demand - demand forecasting and methods of demand forecasting. Isoquants and isocosts — input-output relationship - law of returns - internal and external economies of scale.

Cost Concepts:The book is a must have for all GATE aspirants writing the mathematics paper. Find tbe mean and mode oflbe distribution.

If the distribution is moderately asymmetrical. Or LM PD.. Absolute Moments. Measures 'of Dispersion.

## Business Statistics by [S P Gupta]

Suppose in a draw we pick up balls numbered 2 and 6. If we are given a frequency.. Since the grouped frequency distribution is not continuous. We also feel that the probability of obtaining either a "S" or a "6" in a single throw of a die.

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