真空题。 2.0分) function [0₂ 1/2, F(x)= 3/4 Ⓒ x <0 0
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![**Problem 1: (2 points)**
Given a function \( F(x) \) defined as:
\[
F(x) =
\begin{cases}
0, & x < 0 \\
1/2, & 0 \leq x < 0.5 \\
3/4, & 0.5 \leq x < 2 \\
1, & x \geq 2
\end{cases}
\]
This function is the cumulative distribution function (c.d.f) for some discrete random variable \( X \). Determine the probability mass function (p.m.f) for \( X \).
**Answer:**
**Explanation:**
This problem involves finding the probability mass function (p.m.f) from the given cumulative distribution function (c.d.f) of a discrete random variable \( X \). The c.d.f, \( F(x) \), provides the cumulative probabilities up to certain points, and from these, we can derive the individual probabilities associated with specific values of \( X \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd35023d8-e07b-468b-b1f8-98eea56df46d%2F2f91af4d-ad52-4a02-a9ec-bb6b24c5249e%2F0d5svt_processed.png&w=3840&q=75)
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