5.1.2 WP Show that the following function satisfies the prope ties of a joint probability mass function. y fxy(x, y) -1.0 -2 1/8 -0.5 -1 1/4 0.5 1 1/2 1.0 2 1/8 Determine the following: а. Р(Х <0.5, Y < 1.5) с. Р(Ү < 1.5) e. Е(X), Е(Y), VIX), V(Y) b. Р(X < 0.5) d. P(X > 0.25, Y < 4.5) f. Marginal probability distribution of X
5.1.2 WP Show that the following function satisfies the prope ties of a joint probability mass function. y fxy(x, y) -1.0 -2 1/8 -0.5 -1 1/4 0.5 1 1/2 1.0 2 1/8 Determine the following: а. Р(Х <0.5, Y < 1.5) с. Р(Ү < 1.5) e. Е(X), Е(Y), VIX), V(Y) b. Р(X < 0.5) d. P(X > 0.25, Y < 4.5) f. Marginal probability distribution of X
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:### 5.1.2 Joint Probability Mass Function
This section presents a function for validation against the properties of a joint probability mass function.
#### Joint Distribution Table
| **x** | **y** | **f<sub>XY</sub>(x, y)** |
|--------|-------|--------------------------|
| -1.0 | -2 | 1/8 |
| -0.5 | -1 | 1/4 |
| 0.5 | 1 | 1/2 |
| 1.0 | 2 | 1/8 |
#### Tasks
1. **Marginal Probability Distribution of X**
2. **Determine the following:**
- **a.** \( P(X < 0.5, Y < 1.5) \)
- **b.** \( P(X < 0.5) \)
- **c.** \( P(Y < 1.5) \)
- **d.** \( P(X > 0.25, Y < 4.5) \)
- **e.** \( E(X), E(Y), V(X), V(Y) \)
- **f.** Marginal probability distribution of X
### Additional Information
The data presented in the table represents a discrete joint probability distribution function. The table should be used to find probabilities, expectations, and variances as requested. The function \( f_{XY}(x, y) \) provides the probability for each pair of \( x \) and \( y \).
To complete the tasks, utilize the given joint distribution to compute each required probability and statistical measure.
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