Bonferroni's inequality states that for any two events C₁ and C₂: / बोनफेरोनी की असमिका (Bonferroni's inequality) के अनुसार किन्हीं दो घटनाओं C₁ और C₂ के लिए:

P(C₁ C₂) ≥ P(C₁) + P(C₂) - 1

P(C₁ C₂) ≤ P(C₁) + P(C₂)

P(C₁ C₂) ≤ P(C₁) + P(C₂) - 1

P(C₁ C₂) ≥ P(C₁) + P(C₂) - 1

P(C₁ C₂) = P(C₁) + P(C₂) - 1

बोनफेरोनी की असमिका (Bonferroni's inequality) के अनुसार किन्हीं...

Q.6

ICAR AIEEA PG 2024 - Statistical Sciences (Q.33)

MCQ (Single Correct) +4 −1

If $P(A) = 0.25$, $P(B) = 0.50$ and $P(A \cap B) = 0.14$, then the probability that neither $A$ nor $B$ occurs is:

यदि $P(A) = 0.25$, $P(B) = 0.50$ और $P(A \cap B) = 0.14$ हो, तो न तो $A$ और न ही $B$ के घटित होने की प्रायिकता है:

0.35 0.35 0.61 0.61 0.39 0.39 0.89 0.89

Q.7

ICAR AIEEA PG 2024 - Statistical Sciences (Q.37)

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.8

ICAR AIEEA PG 2024 - Statistical Sciences (Q.38)

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.9

ICAR AIEEA PG 2024 - Statistical Sciences (Q.50)

MCQ (Single Correct) +4 −1

If $A$ and $B$ are two mutually exclusive events with $P(A) > 0$ and $P(B) > 0$, then the conditional probability $P(B|A)$ is:

यदि $A$ और $B$ दो परस्पर अपवर्जी (mutually exclusive) घटनाएं हैं जिनमें $P(A) > 0$ और $P(B) > 0$ है, तो सप्रतिबंध प्रायिकता $P(B|A)$ होगी:

$P(B)$ $P(B)$ 0 0 1 1 $P(A \cap B)$ $P(A \cap B)$

Q.10

ICAR AIEEA PG Statistical Sciences 09 July 2023 (Shift 1) Paper (Q.18)

MCQ (Single Correct) +4 −1

What is the probability of getting a head and a tail in a toss of two coins ?

दो सिक्कों को एक साथ उछालने पर एक चित (Head) और एक पट (Tail) प्राप्त होने की प्रायिकता क्या है?

$0$ $0$ $1$ 1 $0.25$ 25 $0.5$ 5

सक्रिय अध्याय: Probability Theory: Classical, Axiomatic Definitions, Addition, Multiplication Theorems and Bayes Theorem

इस टॉपिक से पूछे गए प्रश्न इन पेपर्स में उपलब्ध हैं:

सामान्य कृषि, कृषि अर्थशास्त्र एवं प्रसार शिक्षा

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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

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Differential Calculus: Limits, Continuity, Differentiability, Successive Differentiation and Expansion of Functions Sequences and Series: Arithmetic, Geometric, Harmonic Progressions and Infinite Series Convergence Matrices and Determinants: Matrix Operations, Rank, Inverse, Systems of Linear Equations and Eigenvalues Sets, Relations, Functions, Mathematical Induction and Theory of Equations Integral Calculus: Definite and Indefinite Integrals, Reduction Formulas and Areas Under Curves Differential Equations: First Order Ordinary Differential Equations, Linear Differential Equations with Constant Coefficients Applications of Derivatives: Tangents, Normals, Maxima-Minima, Mean Value Theorems and Indeterminate Forms Numerical Methods: Interpolation, Numerical Differentiation, Integration (Trapezoidal, Simpson) and Root Finding Coordinate Geometry: Straight Lines, Circles, Parabola, Ellipse and Hyperbola in Two Dimensions

सांख्यिकीय विधियां, प्रायिकता एवं प्रायोगिक अभिकल्पनाएं

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 सक्रिय 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 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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