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Overview Of Random Variable & Probability Distribution Video Lecture | Statistics Optional Videos & Past Year Papers for UPSC
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FAQs on Overview Of Random Variable & Probability Distribution Video Lecture - Statistics Optional Videos & Past Year Papers for UPSC
| 1. What is a random variable and how is it classified? |  |
Ans.A random variable is a numerical outcome of a random phenomenon. It can be classified into two main types: discrete random variables, which take on a countable number of distinct values, and continuous random variables, which can take any value within a given range. For example, the number of heads in a series of coin tosses is a discrete random variable, while the weight of a randomly selected person is a continuous random variable.
| 2. What is a probability distribution and why is it important? | |
Ans.A probability distribution is a mathematical function that provides the probabilities of occurrence of different possible outcomes for a random variable. It is important because it allows us to understand and predict the behavior of random variables. The distribution can be represented in various forms, including probability mass functions for discrete variables and probability density functions for continuous variables.
| 3. How do you calculate the expected value of a random variable? | |
Ans.The expected value, or mean, of a random variable is calculated by multiplying each possible value by its corresponding probability and then summing these products. For a discrete random variable \(X\), the expected value \(E(X)\) is given by the formula \(E(X) = \sum (x_i \cdot P(x_i))\), where \(x_i\) represents the values of the random variable and \(P(x_i)\) their probabilities. For continuous random variables, it is calculated using integration.
| 4. What are the key differences between a discrete and a continuous probability distribution? | |
Ans.The key differences between discrete and continuous probability distributions are based on the nature of the random variable. Discrete probability distributions deal with random variables that have specific, countable outcomes (like rolling a die), whereas continuous probability distributions handle random variables that can take any value within a given interval (like measuring height). Consequently, discrete distributions use probability mass functions, while continuous distributions use probability density functions.
| 5. Can you explain the concept of variance and its significance in probability distributions? | |
Ans.Variance is a measure of how much the values of a random variable differ from the expected value. It quantifies the spread or dispersion of the distribution. The variance \(Var(X)\) is calculated as the expected value of the squared deviation of a random variable from its mean: \(Var(X) = E[(X - E(X))^2]\). A high variance indicates that the values are spread out over a wider range, while a low variance indicates that they are clustered closely around the mean. This is significant as it helps in assessing the risk and volatility associated with random variables.
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Nov 21, 2024 Last updated |
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