Question

Find the CDF of an r.v. $X \sim \operatorname{DUnif}(1,2, \ldots, n) .$

   Find the CDF of an r.v. $X \sim \operatorname{DUnif}(1,2, \ldots, n) .$

Introduction to Probability

Introduction to Probability

Joseph K.… 2nd Edition

Chapter 3, Problem 15

Instant Answer

Solved by Expert Dominador Tan

10/05/2023

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$$ Now, we want to find the cumulative distribution function (CDF) of $X$, which is defined as: $$ F_X(x) = P(X \le x). $$ Show more…

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Find the CDF of an r.v. $X \sim \operatorname{DUnif}(1,2, \ldots, n) .$

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Key Concepts

Discrete Uniform Distribution

A discrete uniform distribution is a probability distribution where a finite number of outcomes are equally likely. Every value within the specified set has the same probability, which makes calculating probabilities straightforward by dividing one by the total number of possible outcomes.

Probability Mass Function (PMF)

The probability mass function for a discrete random variable defines the probability that the variable is exactly equal to a certain value. In a discrete uniform distribution, the PMF assigns an equal probability to each outcome in the support, which is the key to deriving other functions like the CDF.

Cumulative Distribution Function (CDF)

The cumulative distribution function for a discrete random variable gives the probability that the variable takes a value less than or equal to a particular value. It is obtained by summing the probabilities provided by the PMF for all outcomes up to that value, providing a comprehensive picture of the distribution's behavior.

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