Probability Engine · STA210

Statistics II (BSc CSIT, STA210): the questions likely to come

32 analyzed questions from 8 past papers (2074-2082), grouped by syllabus unit — each with its probability, how often it's been asked, and where to study the answer.

Papers analyzed

2074-2082

Analyzed questions

across 6 syllabus units

Very likely units

high-probability topics

Units = 80% of marks

study these first

Model answers for this subject are being written. Every question links to its original paper so you can study from the source meanwhile.

Pick a unit

U1 · Q1/8 · 207910 marks

Probability and Probability Distributions

Define a probability distribution. Explain the binomial distribution with its mean and variance, and state the conditions under which it is applied.

32%

Possible to appearAppeared in 3 of the last 3 board papers

Seen in

How well do you know this?rating moves you on

MODEL ANSWERU1 · 10 marks

Probability Distribution

A probability distribution is a mathematical function (or table) that assigns to each possible value of a random variable the probability of its occurrence. For a discrete random variable $X$ taking values $x_1, x_2, \dots$ it is described by the probability mass function $P(X = x_i) = p_i$ with $p_i \ge 0$ and $\sum_i p_i = 1$ ; for a continuous variable it is described by a probability density function $f(x)$ with $f(x) \ge 0$ and $\int_{-\infty}^{\infty} f(x)\,dx = 1$ .

Binomial Distribution

A discrete random variable $X$ follows a binomial distribution if it counts the number of successes in $n$ independent Bernoulli trials, each having success probability $p$ (and failure $q = 1 - p$ ). Its probability mass function is

P(X = x) = \binom{n}{x} p^{x} q^{\,n-x}, \qquad x = 0, 1, 2, \dots, n.

Mean and Variance

\text{Mean } \mu = E(X) = np, \qquad \text{Variance } \sigma^{2} = npq.

Since $q < 1$ , the variance $npq$ is always less than the mean $np$ , i.e. for the binomial distribution mean $>$ variance.

Outline of the mean: writing $X = \sum_{i=1}^{n} X_i$ where each $X_i$ is Bernoulli with $E(X_i)=p$ , by linearity $E(X)=\sum E(X_i)=np$ ; similarly $\operatorname{Var}(X_i)=pq$ and by independence $\operatorname{Var}(X)=npq$ .

Conditions for Application

The binomial distribution applies when:

The number of trials $n$ is fixed and finite.
Each trial has only two outcomes — success or failure (dichotomous).
The trials are independent of one another.
The probability of success $p$ remains constant from trial to trial.

Examples: number of heads in 10 tosses of a coin, number of defective items in a sample of fixed size, number of correct answers in a multiple-choice test.

AI-generated answer · unverifiedView in 2079 paper →

U1 · Question 1 of 8

Question Priority · U1ranked by appearance likelihood — study top-down

Probability and Probability Distributions

Analyzed next54%

★ TOP PICK

Define a probability distribution. Explain the binomial distribution with its mean and variance, and state the conditions under which it is applied.

10 marksSEEN IN

32%

Define index numbers and explain Laspeyres' and Paasche's price index methods.

5 marksSEEN IN

54%

State and explain the addition and multiplication theorems of probability with examples.

5 marksSEEN IN

52%

Explain the Poisson distribution with its mean and variance and state its applications.

5 marksSEEN IN

52%

Define a random variable. Differentiate between discrete and continuous random variables with examples.

5 marksSEEN IN

52%

Explain the normal distribution and its properties. The mean of a normal distribution is 50 and standard deviation is 10; find the probability that a value lies between 45 and 62.

10 marksSEEN IN

24%

Define mathematical expectation. State and prove its properties.

5 marksSEEN IN

48%

Define stochastic process. In a town each day is either sunny or rainy. A sunny day is followed by another sunny day with probability 0.8, whereas a rainy is followed by sunny day is with probability 0.4. If it rains on Sunday, make forecast for Monday and Tuesday.

5 marksSEEN IN

25%

03The mock

Sit a probable paper

A full mock exam built from the most likely questions, mirroring the real paper's structure. Every slot is a real past question.

Most Probable Paper

Mirrors the real structure · 60 marks · based on 8 past papers

Section A: Long Answer QuestionsAttempt any TWO questions.

1.
What is hypothesis testing? Explain the procedure of testing of hypothesis including null and alternative hypotheses, level of significance, types of errors and the critical region.
[10 marks]
Testing of HypothesisVery likelyfrom 2080 paper →
This question has recurred in 4 of 8 years; so far only in internal assessments, not the board; and its topic (Testing of Hypothesis) appears in 100% of years.
2.
What is sampling? Explain different methods of probability and non-probability sampling with their merits and demerits.
[10 marks]
Sampling and Sampling DistributionsVery likelyfrom 2081 paper →
This question has recurred in 4 of 8 years; so far only in internal assessments, not the board; and its topic (Sampling and Sampling Distributions) appears in 88% of years.
3.
Define a probability distribution. Explain the binomial distribution with its mean and variance, and state the conditions under which it is applied.
[10 marks]
Probability and Probability DistributionsVery likelyfrom 2079 paper →
This question has recurred in 3 of 8 years; so far only in internal assessments, not the board; and its topic (Probability and Probability Distributions) appears in 100% of years.

Section B: Short Answer QuestionsAttempt any EIGHT questions.

1.
Define Karl Pearson's coefficient of correlation and state its properties.
[5 marks]
Correlation and RegressionVery likelyfrom 2081 paper →
This question has recurred in 6 of 8 years; so far only in internal assessments, not the board; and its topic (Correlation and Regression) appears in 88% of years.
2.
What are regression coefficients? State their properties.
[5 marks]
Correlation and RegressionVery likelyfrom 2081 paper →
This question has recurred in 6 of 8 years; so far only in internal assessments, not the board; and its topic (Correlation and Regression) appears in 88% of years.
3.
Explain the concept of sampling distribution and standard error.
[5 marks]
Sampling and Sampling DistributionsVery likelyfrom 2081 paper →
This question has recurred in 6 of 8 years; so far only in internal assessments, not the board; and its topic (Sampling and Sampling Distributions) appears in 88% of years.
4.
Define index numbers and explain Laspeyres' and Paasche's price index methods.
[5 marks]
Probability and Probability DistributionsVery likelyfrom 2081 paper →
This question has recurred in 5 of 8 years; so far only in internal assessments, not the board; and its topic (Probability and Probability Distributions) appears in 100% of years.
5.
State and explain the addition and multiplication theorems of probability with examples.
[5 marks]
Probability and Probability DistributionsVery likelyfrom 2081 paper →
This question has recurred in 5 of 8 years; so far only in internal assessments, not the board; and its topic (Probability and Probability Distributions) appears in 100% of years.
6.
Explain the Poisson distribution with its mean and variance and state its applications.
[5 marks]
Probability and Probability DistributionsVery likelyfrom 2081 paper →
This question has recurred in 5 of 8 years; so far only in internal assessments, not the board; and its topic (Probability and Probability Distributions) appears in 100% of years.
7.
Define a random variable. Differentiate between discrete and continuous random variables with examples.
[5 marks]
Probability and Probability DistributionsVery likelyfrom 2081 paper →
This question has recurred in 5 of 8 years; so far only in internal assessments, not the board; and its topic (Probability and Probability Distributions) appears in 100% of years.
8.
Define mathematical expectation. State and prove its properties.
[5 marks]
Probability and Probability DistributionsVery likelyfrom 2080 paper →
This question has recurred in 5 of 8 years; so far only in internal assessments, not the board; and its topic (Probability and Probability Distributions) appears in 100% of years.
9.
Explain the F-test for the equality of two population variances.
[5 marks]
Testing of HypothesisVery likelyfrom 2081 paper →
This question has recurred in 5 of 8 years; so far only in internal assessments, not the board; and its topic (Testing of Hypothesis) appears in 100% of years.

04The receipts

Behind the numbers

The raw evidence the predictions are computed from: marks per unit per year, syllabus weights, trends, and coverage.

Show the heatmap, topic table and coverage analysis

The receipt: marks per unit, per year

Each row is a syllabus unit, each column an exam year, each cell the marks that unit earned that year. Click any cell to see the actual questions behind it.

Marks:nonefew → many

2074

2075

2077

2078

2079

2080

2081

2082

Total

U1Probability and Probability Distributions

180

U4Testing of Hypothesis

180

U5Correlation and Regression

U2Sampling and Sampling Distributions

U3Estimation

U6Non-Parametric Tests and Statistical Quality Control

#	Syllabus unit	Probability	Appeared	Avg marks	Syllabus weight	Exam vs syllabus	Trend	Questions
1	U1Probability and Probability Distributions	Very likely100%	2074 2075 2077 2078 2079 2080 2081 2082	22.5	22%10 lecture hrs	Over-examinedexam 30% · syllabus 22%	Fading	7 recurring8 total
2	U4Testing of Hypothesis	Very likely100%	2074 2075 2077 2078 2079 2080 2081 2082	22.5	27%12 lecture hrs	Balancedexam 30% · syllabus 27%	Steady	5 recurring12 total
3	U5Correlation and Regression	Very likely88%	2074 2075 2077 2079 2080 2081 2082	12.9	11%5 lecture hrs	Balancedexam 15% · syllabus 11%	Steady	3 recurring4 total
4	U2Sampling and Sampling Distributions	Very likely88%	2074 2075 2077 2079 2080 2081 2082	11.4	18%8 lecture hrs	Balancedexam 13% · syllabus 18%	Steady	2 recurring4 total
5	U3Estimation	Likely75%	2075 2077 2078 2080 2081 2082	10	16%7 lecture hrs	Under-examinedexam 10% · syllabus 16%	Steady	2 recurring3 total
6	U6Non-Parametric Tests and Statistical Quality Control	Occasional12%	2082	10	7%3 lecture hrs	Balancedexam 2% · syllabus 7%	Rising	none repeat1 total

Study smart, not hard

Drag the slider: studying the top 4 units in priority order covers ~88% of all observed marks.

Units to study4/6

~80% line

Lecture time vs exam marks

Where the exam pays more than the curriculum spends: ● lectures vs ● exam marks, as a share of the whole course. A long teal-leading bar = high-yield unit.

U1Probability and Probability Distributions

22% of lectures → 30% of markshigh yield

U4Testing of Hypothesis

27% of lectures → 30% of marks

U5Correlation and Regression

11% of lectures → 15% of marks

U2Sampling and Sampling Distributions

18% of lectures → 13% of marks

U3Estimation

16% of lectures → 10% of markslow yield

U6Non-Parametric Tests and Statistical Quality Control

7% of lectures → 2% of marks

Statistics II (BSc CSIT, STA210): the questions likely to come

Probability Distribution

Binomial Distribution

Conditions for Application

Probability and Probability Distributions

Sit a probable paper

Most Probable Paper

Behind the numbers

The receipt: marks per unit, per year

Study smart, not hard

Lecture time vs exam marks

2082 B.S.

Statistics II (BSc CSIT, STA210)

2081 B.S.

Statistics II (BSc CSIT, STA210)

2080 B.S.

Statistics II (BSc CSIT, STA210)

2079 B.S.

Statistics II (BSc CSIT, STA210)

2078 B.S.

Statistics II (BSc CSIT, STA210)

2077 B.S.

Statistics II (BSc CSIT, STA210)

2075 B.S.

Statistics II (BSc CSIT, STA210)

2074 B.S.

Statistics II (BSc CSIT, STA210)