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Theoretical Distributions - 2 Video Lecture | Crash Course for CA Foundation

FAQs on Theoretical Distributions - 2 Video Lecture - Crash Course for CA Foundation

1. What are the main types of theoretical distributions used in statistics?

Ans. The main types of theoretical distributions include the Normal distribution, Binomial distribution, Poisson distribution, Exponential distribution, and Uniform distribution. Each of these distributions has specific properties and applications depending on the nature of the data and the scenario being analyzed.

2. How does the Normal distribution differ from the Binomial distribution?

Ans. The Normal distribution is a continuous distribution that is symmetric and bell-shaped, often used to model real-valued random variables with a mean and standard deviation. In contrast, the Binomial distribution is a discrete distribution that models the number of successes in a fixed number of independent Bernoulli trials, characterized by two outcomes (success or failure).

3. What is the significance of the Central Limit Theorem in relation to theoretical distributions?

Ans. The Central Limit Theorem states that the distribution of the sample mean of a sufficiently large number of independent random variables will approximate a Normal distribution, regardless of the original distribution of the variables. This theorem is significant because it allows statisticians to make inferences about population parameters using the Normal distribution, even when the population distribution is not normal.

4. When would you use a Poisson distribution in practical applications?

Ans. A Poisson distribution is used for modeling the number of events occurring within a fixed interval of time or space, given that these events happen with a known constant mean rate and independently of the time since the last event. Common applications include predicting the number of phone calls received by a call center in an hour or the number of decay events per unit time from a radioactive source.

5. Can you explain the concept of expected value in the context of theoretical distributions?

Ans. The expected value, or mean, of a theoretical distribution is a measure of the central tendency of the distribution. It represents the average outcome one would expect if an experiment were repeated a large number of times. For discrete distributions, it is calculated by summing the products of each outcome and its probability, while for continuous distributions, it involves integrating over the range of possible values, weighted by the probability density function.

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Sep 09, 2025 Last updated

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