CA 225(B) : Basics of Statistics and Probability for Computer Science
1. Introduction to Statistics
1.1 Meaning of Statistics
1.2 Importance and Limitations of Statistics
1.3 Meaning of Data, Raw Data, Primary Data, Secondary Data, Variable and Attribute
1.4 Types of Variables: Districts and Continuous, Meaning Of Population and Sample
1.5 Introduction to Methods of Sampling: Simple Random Sampling and Stratified Random Sampling
2. Measures of Central Tendency
2.1 Meaning and Central Tendency
2.2 Statement of Measures of Central Tendency: Arithmetic Mean, Geometric Mean, Harmonic Mean, Median and Mode
2.3 Computation of These Measures of Central Tendency for Given Raw Data
2.4 Partition Values: Quartiles, Deciles and Percentiles
2.5 Computation of Partition Values for Given Raw Data
3. Introduction to Probability
3.1 Basic Concepts of Probability: Definitions: Experiment, Sample Space, Events
3.2 Types of Events: Simple, Compound, Mutually Exclusive, and Exhaustive
3.3 Classical Probability
3.4 Axioms of Probability: Non-Negativity, Additivity
3.5 Applications and Examples
4. Conditional Probability and Independence
4.1 Conditional Probability
4.2 Independent Events
4.3 The Law of Total Probability
4.4 Bayes’ Theorem
CA-226(B) : Practical on Basics of Statistics and Probability for Computer Science
1) Use the dataset of the ages of 50 employees in a ABC pvt. Ltd. company.
i. Classify the data as primary (collected first hand) or secondary (obtained from existing sources).
ii. Determine whether the age variable is discrete (countable values) or continuous (any value within a range).
2) Consider a dataset containing information on students: age, gender, test scores, and participation in extracurricular activities.
i. Identify which variables are quantitative (e.g., age, test scores) and which are qualitative (e.g., gender, participation).
ii. Determine which variables are discrete (e.g., number of activities) and which are continuous (e.g., test scores).
3) Given the test scores of 10 students: 72, 85, 90, 75, 88, 95, 80, 78, 84, and 91.
i. Compute the arithmetic mean (average) of the scores.
ii. Calculate the median (middle value) of the scores.
iii. Determine the mode (most frequent score) if it exists.
4) Using the same dataset of test scores: 72, 85, 90, 75, 88, 95, 80, 78, 84, 91.
i. Calculate the first quartile (Q1), median (Q2), and third quartile (Q3).
ii. Determine the 20th percentile (P20) and 80th percentile (P80) of the scores.
5) Consider the experiment of rolling a six-sided die.
i. Define the sample space (S) for the experiment.
ii. Identify events such as rolling an even number (E) and rolling a number greater than 4 (G).
6) In a standard deck of 52 cards, calculate the probability of drawing an Ace.
i. Determine the number of favourable outcomes (drawing an Ace) and the total number of possible outcomes (52 cards).
ii. Compute the probability as the ratio of favourable outcomes to total outcomes.
7) In a deck of 52 cards, what is the probability of drawing a King given that a face card has been drawn?
i. Identify the number of face cards in the deck (Jack, Queen, and
King of each suit: 12 cards).
ii. Determine the number of Kings among the face cards (4 Kings).
8) Consider two events: A = drawing a red card from a deck, and B = drawing a King.
i. Calculate the probability of event A (drawing a red card).
ii. Calculate the probability of event B (drawing a King).
iii. Determine if events A and B are independent by checking if P(A ∩ B) = P(A) * P(B).
9) A factory produces 60% of its products from Machine A and 40% from Machine B. The defect rates are 3% for Machine A and 5% for Machine B. If a randomly selected product is found to be defective, what is the probability it was produced by Machine A?
i. Define events: D = defective product, A = product from Machine A, B = product from Machine B.
