https://file.aiquickdraw.com/mathbot/file/1726353170958espp1ku1.jpg

The statement in the question refers to \( X \) as the weight of a gear in grams, with a probability density function (pdf) \( f(x) = \frac{1}{3} \) over the range \( 3.5 < x < 6.5 \) grams. The problem asks if \( X \) is a **discrete random variable**.

Let's break this down:

1. A **discrete random variable** takes on countable values (like integers).
2. A **continuous random variable**, on the other hand, can take any value within a certain range.

Since the given probability density function is constant over the interval \( 3.5 < x < 6.5 \), and \( X \) can take any value within this continuous range, \( X \) is a **continuous random variable**, not a discrete one.

Thus, the correct answer is **False**.

Would you like more details or have any questions?

Here are 5 relative questions to expand on this:
1. What are the key differences between discrete and continuous random variables?
2. How do you interpret a probability density function (pdf)?
3. What are some real-world examples of discrete random variables?
4. What is the total probability for a pdf over its defined range?
5. How would the pdf change if the range of \( X \) was larger or smaller?

**Tip:** Always check whether the random variable's possible outcomes are countable (discrete) or uncountable (continuous) when determining its type.

X is the weight, in grams, of a gear used in the rotary mechanism of a microwave oven. The pdf is given as f(x) = 1/3 for 3.5 grams < x < 6.5 grams. X is a discrete random variable. True or False?

This problem explores whether X, the weight of a gear with a pdf of f(x) = 1/3 for 3.5 < x < 6.5 grams, is a discrete or continuous random variable. Learn about probability density functions (pdf) and the distinctions between discrete and continuous random variables.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation