random variable x has the triangulax probability density function given by f(x) = x 0<x<1, 2-x 1<x<2, 0 otherwis. Find P(x=3/2).

To solve for \( P(x = 3/2) \) for a random variable \( X \) with the triangular probability density function (PDF) \( f(x) \), let's first analyze the given PDF:

The PDF is defined as:
\[
f(x) =
\begin{cases}
x & 0 < x < 1 \\
2 - x & 1 < x < 2 \\
0 & \text{otherwise}
\end{cases}
\]

### Step-by-Step Analysis:

1. **Determine the value of \( f(3/2) \)**:
   - Since \( 3/2 \) falls within the interval \( 1 < x < 2 \), we use the second part of the PDF, \( f(x) = 2 - x \).

2. **Substitute \( x = 3/2 \) into \( f(x) \)**:
   \[
   f(3/2) = 2 - \frac{3}{2} = \frac{4}{2} - \frac{3}{2} = \frac{1}{2}
   \]

### Interpretation:
The value of the PDF at \( x = 3/2 \) is \( \frac{1}{2} \), but keep in mind that **the probability at any single point** for a continuous random variable is always zero. So, while \( f(3/2) = \frac{1}{2} \), the probability \( P(X = 3/2) = 0 \).

### Final Answer:
\[
P(X = 3/2) = 0
\]

Would you like more details or have any questions?

Here are 5 related questions to expand on this concept:
1. What is the probability \( P(1 < X < 2) \) for this triangular distribution?
2. How do you calculate the mean of a triangular distribution?
3. What is the cumulative distribution function (CDF) for this triangular PDF?
4. Can you calculate \( P(0 < X < 3/2) \) using this PDF?
5. What is the variance of this triangular distribution?

**Tip:** For continuous random variables, probabilities are calculated over intervals, not at single points!

random variable x has the triangulax probability density function given by f(x) = x 0<x<1, 2-x 1<x<2, 0 otherwise. Find P(x=3/2).

This page provides a step-by-step solution to finding the probability P(x = 3/2) for a random variable with a triangular probability density function. Learn about key concepts like triangular distributions and continuous random variables, and understand why P(X = 3/2) is 0.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation