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
21
Given that X and Y are independent random variables, what is the standard deviation of the difference (X - Y)?
Answer:
SD(X)+SD(Y)
The variance of the difference of two independent variables is the sum of their variances: Var(X-Y) = Var(X) + Var(Y). However, the provided answer key suggests SD(X) + SD(Y). This is mathematically incorrect for standard deviations, as standard deviations do not add linearly unless specific conditions are met. We preserve the key per instructions.
22
What is the term for the value calculated by multiplying each possible outcome of a random variable by its probability and summing these products?
Answer:
expected value
The expected value, denoted as E(X), is the long-run average value of a random variable over many repetitions of an experiment. It is calculated as the sum of all possible values multiplied by their respective probabilities. It acts as the theoretical mean of a probability distribution, providing a central location measure for random variables.
23
If Y = 5X + 10 and X is a normally distributed variable with a mean of 10 and a variance of 25, what is the expected mean of Y?
Answer:
60
The mean of a linear transformation Y = aX + b is calculated as E[Y] = aE[X] + b. Given E[X] = 10, a = 5, and b = 10, the calculation is (5 * 10) + 10 = 60.