Please answer the whole question quickly and correctly Two close friends live in different continents. Let X be the number of years between two consecutive meetings of two friends. The cumulative distribution function of random variable X is as follows: a. Is X discrete or continuous random variable? b. If X is discrete, find its pmf. If X is continuous, find its pdf. c. What is? d. What is? e. What is

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Please answer the whole question quickly and correctly Two close friends live in different continents. Let X be the number of years between two consecutive meetings of two friends. The cumulative distribution function of random variable X is as follows: a. Is X discrete or continuous random variable? b. If X is discrete, find its pmf. If X is continuous, find its pdf. c. What is? d. What is? e. What is?
The image presents a piecewise function \( F(x) \) defined by various conditions for \( t \). The function \( F(x) \) is specified as follows:

\[
F(x) =
\begin{cases}
0, & t < 2 \\
\frac{1}{2}, & 2 \leq t < 4 \\
\frac{3}{4}, & 4 \leq t < 6 \\
\frac{15}{16}, & 6 \leq t < 8 \\
1, & t \geq 8 
\end{cases}
\]

**Explanation:**
1. **\( t < 2 \):** The function \( F(x) \) equals 0.
2. **\( 2 \leq t < 4 \):** The function \( F(x) \) equals \(\frac{1}{2}\).
3. **\( 4 \leq t < 6 \):** The function \( F(x) \) equals \(\frac{3}{4}\).
4. **\( 6 \leq t < 8 \):** The function \( F(x) \) equals \(\frac{15}{16}\).
5. **\( t \geq 8 \):** The function \( F(x) \) equals 1.

This piecewise function defines \( F(x) \) with different constant values over distinct intervals of the variable \( t \).
Transcribed Image Text:The image presents a piecewise function \( F(x) \) defined by various conditions for \( t \). The function \( F(x) \) is specified as follows: \[ F(x) = \begin{cases} 0, & t < 2 \\ \frac{1}{2}, & 2 \leq t < 4 \\ \frac{3}{4}, & 4 \leq t < 6 \\ \frac{15}{16}, & 6 \leq t < 8 \\ 1, & t \geq 8 \end{cases} \] **Explanation:** 1. **\( t < 2 \):** The function \( F(x) \) equals 0. 2. **\( 2 \leq t < 4 \):** The function \( F(x) \) equals \(\frac{1}{2}\). 3. **\( 4 \leq t < 6 \):** The function \( F(x) \) equals \(\frac{3}{4}\). 4. **\( 6 \leq t < 8 \):** The function \( F(x) \) equals \(\frac{15}{16}\). 5. **\( t \geq 8 \):** The function \( F(x) \) equals 1. This piecewise function defines \( F(x) \) with different constant values over distinct intervals of the variable \( t \).
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