Statistics MCQs
Topic Notes: Statistics
MCQs and preparation resources for competitive exams, covering important concepts, past papers, and detailed explanations.
Plato
- Biography: Ancient Greek philosopher (427–347 BCE), student of Socrates and teacher of Aristotle, founder of the Academy in Athens.
- Important Ideas:
- Theory of Forms
- Philosopher-King
- Ideal State
1
What condition must the second degrees of freedom (n2) satisfy for the variance of an F-distribution to exist?
Answer:
n2> 4
The F-distribution is defined by two parameters, n1 and n2, representing the degrees of freedom for the numerator and denominator respectively. The variance of the F-distribution is given by a formula that involves terms with (n2-2) and (n2-4) in the denominator. Therefore, for the variance to be finite and well-defined, n2 must be strictly greater than 4.
2
What is the defining characteristic of the cumulative distribution function (CDF) for a random variable X?
Answer:
From smallest upto specific value of x
The cumulative distribution function (CDF), denoted as F(x), represents the probability that a random variable X takes a value less than or equal to x. It is calculated by accumulating probabilities from the smallest possible value of the variable up to the specific value x, resulting in a non-decreasing function ranging from 0 to 1.
3
What is the term for the probability that a random variable takes on a value less than or equal to a specific point?
Answer:
cumulative probability
Cumulative probability refers to the probability that a random variable X will take a value less than or equal to x. It is represented by the cumulative distribution function (CDF), denoted as F(x) = P(X ≤ x), which accumulates the probabilities of all outcomes up to that point.
4
How is a response variable formally classified in statistical theory?
Answer:
Random variable
A response variable is considered a random variable because its value is subject to uncertainty and variation due to sampling or measurement error. In regression models, we assume the response variable follows a probability distribution, making it a stochastic component rather than a fixed constant.
5
When classifying probability distributions based on their functional characteristics, which categories are typically included?
Answer:
both b and c
Probability distributions are primarily classified based on the nature of the random variable they describe. Discrete distributions are used for countable outcomes, while continuous distributions are used for measurements on a continuous scale. Both are fundamental categories in probability theory.
6
A random variable can be classified into which of the following categories?
Answer:
discrete or continuous
Random variables are categorized based on the nature of the values they can assume. A discrete random variable takes on a countable number of distinct values, whereas a continuous random variable can take on any value within a specified interval. Therefore, a random variable is generally classified as either discrete or continuous.
7
A random variable is defined as a variable whose value is determined by the outcome of which process?
Answer:
Random experiment
A random variable is a numerical mapping of the outcomes of a random experiment. Because the experiment's outcome is subject to chance, the value assigned to the random variable is also subject to chance, making it a fundamental concept in probability theory.
8
What is the name of the function that provides the probability that a random variable X takes a value less than or equal to x?
Answer:
Distribution function
The function that defines the probability P(X ≤ x) for any real number x is known as the cumulative distribution function (CDF). It is frequently referred to as the distribution function. This function provides a complete description of the probability distribution of a random variable, whether it is discrete, continuous, or a mixture of both.
9
A discrete random variable is defined over which type of sample space?
Answer:
Discrete
A discrete random variable is a function mapping outcomes from a sample space to a set of discrete numerical values. For the variable to be discrete, the underlying sample space must consist of countable or distinct individual points, allowing the variable to take on specific, non-overlapping values.
10
Which category of random variable is associated with the normal distribution?
Answer:
Continuous
The normal distribution is a continuous probability distribution. This means the random variable can take on any value within an infinite range of real numbers. Unlike discrete distributions, which are defined for countable outcomes, continuous distributions use probability density functions to describe the likelihood of the variable falling within a specific interval.