UPSC Exam > UPSC Videos > Statistics Optional Videos & Past Year Papers for UPSC > Random Variable, Probability Mass Function, Distribution Function
Random Variable, Probability Mass Function, Distribution Function Video Lecture | Statistics Optional Videos & Past Year Papers for UPSC
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FAQs on Random Variable, Probability Mass Function, Distribution Function 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 types: discrete random variables, which take on a countable number of values, and continuous random variables, which can take on any value within a given interval.
| 2. What is a Probability Mass Function (PMF)? | |
Ans.A Probability Mass Function (PMF) is a function that gives the probability that a discrete random variable is equal to a specific value. It is defined for discrete random variables and must satisfy two conditions: the probabilities must be non-negative, and the sum of all probabilities must equal 1.
| 3. How do you calculate the cumulative distribution function (CDF)? | |
Ans.The cumulative distribution function (CDF) of a random variable is calculated by summing the probabilities of the random variable being less than or equal to a certain value. For a discrete random variable X, the CDF is defined as \( F(x) = P(X \leq x) = \sum_{t \leq x} P(X = t) \).
| 4. What is the relationship between PMF and CDF for discrete random variables? | |
Ans.The relationship between PMF and CDF for discrete random variables is that the CDF can be obtained by summing up the PMF values. Specifically, the CDF at a point x is equal to the sum of the PMF values for all outcomes less than or equal to x.
| 5. What are some common applications of random variables in statistics? | |
Ans.Random variables are commonly used in statistics for various applications, such as modeling uncertainty in experiments, conducting hypothesis testing, analyzing risk in finance, and making predictions in machine learning. They help quantify and analyze variability in data.
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