JKBOSE Class 12th All Subject Notes
JKBOSE Class 12th Statistics Important Textual Questions
What is probability and how is it defined?
Probability is a fundamental concept in mathematics and statistics that quantifies the likelihood of an event occurring. It is defined as a number between 0 and 1 where 0 represents impossibility and 1 represents certainty. The probability of an event A denoted as P(A) measures the relative likelihood of A occurring.
What are the axioms of probability?
The axioms of probability are a set of fundamental principles that govern the behavior of probabilities. There are three axioms: non-negativity (probability of any event is a non-negative number) normalization (probability of the entire sample space is equal to 1) and additivity (probability of the union of mutually exclusive events is equal to the sum of their individual probabilities).
What is conditional probability and how is it calculated?
Conditional probability is a measure of the probability of an event occurring given that another event has already occurred. It is denoted as P(A|B) where A and B are two events. The conditional probability of A given B is calculated by dividing the probability of the intersection of A and B by the probability of event B assuming that P(B) > 0. It is defined as P(A|B) = P(A ∩ B) / P(B).
What is regression analysis and how does it work?
Regression analysis is a statistical concept used to analyze the relationship between variables. It aims to predict the value of a dependent variable based on one or more independent variables. In linear regression a line (regression line) is fitted to a scatterplot of data points to approximate the relationship between variables. The regression line represents the best fit to the data minimizing the distance between the line and the actual data points.
What are index numbers and how are they used?
Index numbers are statistical tools that measure changes in a variable over time. They provide a way to compare different observations or sets of data relative to a base period or reference point. Index numbers are commonly used in economics finance and other fields to track changes in prices quantities or other measurable factors. They help in measuring inflation analyzing stock market performance tracking economic indicators and calculating cost-of-living adjustments.