यदि यादृच्छिक चर X का प्रायिकता घनत्व फलन (pdf) f(x) = {1}{{2π}}... | Agrigyan

सभी विषय सामान्य कृषि, कृषि अर्थशास्त्र एवं प्रसार शिक्षा उच्च गणित: बीजगणित, कलन एवं अवकल समीकरण सांख्यिकीय विधियां, प्रायिकता एवं प्रायोगिक अभिकल्पनाएं कंप्यूटर अनुप्रयोग, प्रोग्रामिंग एवं जैव सूचना विज्ञान

Q.36

ICAR AIEEA PG 2024 - Statistical Sciences

MCQ (Single Correct) +4 −1

A die is thrown 100 times. If getting an even number is considered a success, then the variance of the number of successes is:

एक पासे को 100 बार फेंका जाता है। यदि सम संख्या (even number) प्राप्त करने को सफलता माना जाए, तो सफलताओं की संख्या का प्रसरण (variance) होगा:

50 50 25 25 10 10 5 5

Q.37

ICAR AIEEA PG 2024 - Statistical Sciences

MCQ (Single Correct) +4 −1

Bonferroni's inequality states that for any two events $C_1$ and $C_2$:

बोनफेरोनी की असमिका (Bonferroni's inequality) के अनुसार किन्हीं दो घटनाओं $C_1$ और $C_2$ के लिए:

$P(C_1 \cap C_2) \le P(C_1) + P(C_2)$ $P(C_1 \cap C_2) \le P(C_1) + P(C_2)$ $P(C_1 \cap C_2) \le P(C_1) + P(C_2) - 1$ $P(C_1 \cap C_2) \le P(C_1) + P(C_2) - 1$ $P(C_1 \cap C_2) \ge P(C_1) + P(C_2) - 1$ $P(C_1 \cap C_2) \ge P(C_1) + P(C_2) - 1$ $P(C_1 \cap C_2) = P(C_1) + P(C_2) - 1$ $P(C_1 \cap C_2) = P(C_1) + P(C_2) - 1$

Q.38

ICAR AIEEA PG 2024 - Statistical Sciences

MCQ (Single Correct) +4 −1

A bowl contains 8 chips, 3 marked Red and 5 marked Blue. Two chips are drawn at random without replacement. What is the probability that the first chip is Red and the second chip is Blue?

एक पात्र में 8 चिप्स हैं, जिनमें 3 लाल (Red) और 5 नीली (Blue) हैं। बिना प्रतिस्थापन (without replacement) के यादृच्छिक रूप से दो चिप्स निकाली जाती हैं। पहली चिप लाल और दूसरी चिप नीली होने की प्रायिकता क्या है?

0.27 0.27 0.38 0.38 0.50 0.50 0.15 0.15

Q.39

ICAR AIEEA PG 2024 - Statistical Sciences

MCQ (Single Correct) +4 −1

If the random variable $X$ has normal distribution with probability density function $f(x) = \frac{1}{\sqrt{2\pi}} e^{-(x-1)^2/2}, -\infty < x < \infty$, then the value of $\int_1^\infty f(x) dx$ is:

यदि यादृच्छिक चर $X$ का प्रायिकता घनत्व फलन (pdf) $f(x) = \frac{1}{\sqrt{2\pi}} e^{-(x-1)^2/2}, -\infty < x < \infty$ के साथ प्रसामान्य बंटन (normal distribution) है, तो समाकल $\int_1^\infty f(x) dx$ का मान है:

1 1 1/2 1/2 1/4 1/4 0 0

Q.40

ICAR AIEEA PG 2024 - Statistical Sciences

MCQ (Single Correct) +4 −1

The annual rainfall at a place is normally distributed with mean 1200 mm and standard deviation 200 mm. What is the probability that in a randomly selected year, the rainfall will be greater than 1400 mm? [Given that the area under the standard normal curve between $Z = 0$ and $Z = 1$ is 0.34]

एक स्थान पर वार्षिक वर्षा प्रसामान्य रूप से बंटित है जिसका माध्य 1200 मिमी और मानक विचलन 200 मिमी है। यादृच्छिक रूप से चुने गए वर्ष में वर्षा 1400 मिमी से अधिक होने की प्रायिकता क्या है? [दिया गया है कि मानक प्रसामान्य वक्र के तहत $Z = 0$ और $Z = 1$ के बीच का क्षेत्रफल 0.34 है]

0.16 0.16 0.34 0.34 0.84 0.84 0.50 0.50

सामान्य कृषि, कृषि अर्थशास्त्र एवं प्रसार शिक्षा 12
उच्च गणित: बीजगणित, कलन एवं अवकल समीकरण 48
सांख्यिकीय विधियां, प्रायिकता एवं प्रायोगिक अभिकल्पनाएं 46
कंप्यूटर अनुप्रयोग, प्रोग्रामिंग एवं जैव सूचना विज्ञान 14

सामान्य कृषि, कृषि अर्थशास्त्र एवं प्रसार शिक्षा

8 टॉपिक्स

Agronomy, Agro-Climatic Zones, Cropping Systems, Tillage and Soil Fertility Management Major Plant Diseases, Insect Pests, Weeds and Integrated Pest Management (IPM) Plant Physiology, Mineral Nutrition, Genetics and Plant Breeding Fundamentals Historical Milestones, Agricultural Research Infrastructure and ICAR Institutes Micro & Macro Economics: Demand, Supply, Production Costs and Market Structures Agricultural Marketing, Market Intermediaries, Price Policy, MSP and Buffer Stocking Agricultural Finance, Credit Institutions (NABARD, RRBs, Commercial Banks) and KCC Extension Education Principles, Rural Development Programs and Community Reconstruction

उच्च गणित: बीजगणित, कलन एवं अवकल समीकरण

9 टॉपिक्स

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14 टॉपिक्स

Theoretical Discrete Probability Distributions: Bernoulli, Binomial, Poisson, Geometric and Hypergeometric Design of Experiments: Principles of Experimentation, CRD, RBD, Latin Square Design (LSD) and Factorial Experiments Probability Theory: Classical, Axiomatic Definitions, Addition, Multiplication Theorems and Bayes Theorem Small Sample Tests: Students t-test, Snedecors F-test, Chi-Square Test of Goodness of Fit and Contingency Tables Measures of Central Tendency: Arithmetic Mean, Geometric Mean, Harmonic Mean, Median and Mode Theoretical Continuous Probability Distributions: Uniform, Normal, Exponential, Beta and Gamma Distributions सक्रिय Sampling Theory: Census vs Sample Survey, Sampling Errors, SRSWOR, SRSWR, Stratified, Systematic and Cluster Sampling Measures of Dispersion: Range, Quartile Deviation, Mean Deviation, Standard Deviation and Coefficient of Variation Testing of Hypotheses: Null and Alternative Hypotheses, Type I and II Errors, Significance Level, Large Sample Tests (Z-test) Collection, Classification and Tabulation of Data, Frequency Distributions and Graphical Representations Regression Analysis: Simple and Multiple Linear Regression, Least Squares Principle, Properties and R-Squared Random Variables, Probability Mass and Density Functions, Expectation and Moment Generating Functions Correlation Analysis: Simple, Partial, Multiple Correlation, Pearson Coefficient and Rank Correlation Moments, Skewness (Karl Pearson, Bowley) and Kurtosis

कंप्यूटर अनुप्रयोग, प्रोग्रामिंग एवं जैव सूचना विज्ञान

10 टॉपिक्स

Computer Networks and Internet: Topologies (LAN, WAN, MAN), OSI Model, TCP/IP, Protocols (HTTP, FTP) and Web Computer Architecture and Hardware: Generations of Computers, CPU, Memory Hierarchy (RAM, ROM, Cache), Input-Output System Software and Operating Systems: Functions of OS, DOS Commands, Windows OS, Linux/Unix Architecture Application Software: Word Processing, Spreadsheets (MS Excel Formulas, Functions, Charts), DBMS Basics Number Systems and Boolean Algebra: Binary, Octal, Hexadecimal Conversions, Logic Gates and Truth Tables Sequence Alignment and Computational Genomics: Pairwise and Multiple Alignment (BLAST, FASTA, Clustal), Scoring Matrices Cyber Security and Data Protection: Computer Viruses, Malware, Firewalls, Cryptography Basics and IPR Programming Fundamentals: Algorithms, Flowcharts, Control Structures, Loops, Functions, Arrays and Pointers in C/C++ Object-Oriented Programming and Modern Languages: Concepts of OOP (Classes, Objects, Inheritance), Python and R Introduction to Bioinformatics: Scope, Biological Databases (NCBI, GenBank, EMBL, UniProt, PDB) and Data Retrieval

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