Probability and Statistics
Semester III · BCA 205 · 3 credits
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chapters done
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The syllabus asks for
- Meaning, scope and limitations
- Types of data and variables
- Sources of data
- Methods of collecting primary data
- Seeing the structure of data
- Eight reasons why every computing student needs statistics
Key points
- Statistics collects, organises, analyses and interprets data; it is powerful but limited to aggregates and can be misused.
- Data are qualitative or quantitative and measured on nominal, ordinal, interval or ratio scales.
- Primary data come from surveys, interviews, observation and experiments; secondary data from existing records; each has typical problems.
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The syllabus asks for
- Measures of central tendency
- Measures of dispersion
- Pictures of centre and spread
- Eight uses of averages and measures of spread
Key points
- Mean, median and mode locate the centre; quartiles, deciles and percentiles split the data.
- Range, QD, MD, variance, standard deviation and CV measure spread; CV compares different data sets.
- The median resists outliers; the standard deviation is the standard measure of spread.
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The syllabus asks for
- Correlation
- Regression analysis
- Seeing correlation and regression
- Eight uses of correlation and regression
Key points
- Correlation measures linear association with r from −1 to +1; correlation does not prove causation.
- Least squares regression gives the best-fitting line for predicting y from x; the two regression lines meet at the means and their slopes multiply to r^2.
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The syllabus asks for
- Basic definitions
- Two basic laws
- Conditional probability and Bayes' theorem
- Random variables and probability distributions
- Pictures of probability
- Eight uses of probability and distributions
Key points
- Probability follows the addition and multiplication laws; conditioning updates probabilities and Bayes' rule inverts them.
- Binomial models fixed trials, Poisson rare events, normal measurements, which are standardised to Z for table lookup.
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The syllabus asks for
- Population and sample; census versus sample survey
- Organising a sample survey
- Sample selection and determining the sample size
- Sampling and non-sampling errors
- Pictures of a sample survey
- Eight rules of a good sample survey
Key points
- A sample survey is faster and cheaper than a census; its quality depends on the frame, the design, the questionnaire, the sample size and the control of errors.
- Sample size for a proportion follows n0 = fracz^2 p (1 - p)e^2 with a finite-population correction.
- Sampling error is random and shrinks with n; non-sampling errors are systematic and need careful procedures.
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The syllabus asks for
- Types of sampling
- Simple random sampling (SRS)
- Stratified random sampling
- Systematic sampling
- Cluster and multistage sampling
- Probability proportional to size (PPS) sampling
- Ratio and regression methods of estimation
- Sampling distributions: z, t and χ²
- Pictures of sampling designs and sampling distributions
- Eight sampling designs and tools, and what each is used for
Key points
- SRS is the baseline; stratification gains precision from homogeneous strata; systematic sampling is simple but pattern-sensitive; cluster and multistage designs cut cost; PPS handles unequal clusters.
- Ratio and regression estimators exploit an auxiliary variable.
- The CLT justifies z ; t replaces z for small n with unknown σ ; chi^2 tests counts.
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The syllabus asks for
- Concept of analysis of variance
- The F statistic and its distribution
- The linear model
- One-way classification
- Two-way classification (one observation per cell)
- Pictures of ANOVA and experimental design
- Eight uses of ANOVA and designed experiments
Key points
- ANOVA compares several means by splitting total variation into between and within parts and testing their ratio with the F distribution.
- One-way ANOVA handles one factor; two-way ANOVA adds a blocking factor to reduce error.
- A significant F says means differ somewhere; follow-up tests locate the difference.
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The paper
TU assessment: 60% final examination set by the university, 40% internal (assignments, lab work, attendance). Confirm the split in your college's notice.
Where the hours go
Teaching hours are the board's guide to how much of the paper each part carries.
- Unit 6 · Sample Survey Methods10 h
- Unit 4 · Probability8 h
- Unit 2 · Descriptive Statistics6 h
- Unit 3 · Correlation and Regression Analysis6 h
- Unit 5 · Sample Survey6 h
- Unit 7 · Design of Experiment6 h
- Unit 1 · Introduction to Statistics3 h