the probability

MATLAB: An Introduction with Applications
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### Probability Question on Continuous Random Variable

Consider a continuous random variable \( X \).

Let \( f(x) = c(1 + x^2) \) for support \( S_x = [0, 1] \) and \( c \) being a constant.

#### Question:
What is the probability that \( X \) is equal to exactly \( 0.5 \)?

#### Options:
- \( \circ \) 0
- \( \circ \) 1
- \( \circ \) 0.75

---

### Explanation:
For a continuous random variable, the probability of the variable taking any exact value is always zero. This is because the probability density function (pdf) describes probabilities over intervals, not specific points.

Thus, the correct answer is:
- \( \circ \) 0

### Graphs and Diagrams:
There are no graphs or diagrams included in this question. 

This question emphasizes understanding the properties of continuous random variables and their probability density functions.
Transcribed Image Text:### Probability Question on Continuous Random Variable Consider a continuous random variable \( X \). Let \( f(x) = c(1 + x^2) \) for support \( S_x = [0, 1] \) and \( c \) being a constant. #### Question: What is the probability that \( X \) is equal to exactly \( 0.5 \)? #### Options: - \( \circ \) 0 - \( \circ \) 1 - \( \circ \) 0.75 --- ### Explanation: For a continuous random variable, the probability of the variable taking any exact value is always zero. This is because the probability density function (pdf) describes probabilities over intervals, not specific points. Thus, the correct answer is: - \( \circ \) 0 ### Graphs and Diagrams: There are no graphs or diagrams included in this question. This question emphasizes understanding the properties of continuous random variables and their probability density functions.
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