7. What is the significance of writing the domains in the following ways, what will be different about their graphs? Option 1: y = 3x - 2 , for all Integers of x: -2 to 4 and Option 2: y= 3x - 2, for all real numbers of x: - 2
Addition Rule of Probability
It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.
Expected Value
When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).
Probability Distributions
Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.
Basic Probability
The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.
![**Question 7: What is the significance of writing the domains in the following ways, and what will be different about their graphs?**
**Option 1:**
\[ y = 3x - 2, \text{ for all integers of } x: -2 \text{ to } 4 \]
**and**
**Option 2:**
\[ y = 3x - 2, \text{ for all real numbers of } x: -2 \leq x \leq 4 \]
### Explanation:
In **Option 1**, the function \( y = 3x - 2 \) is defined for all integer values of \( x \) within the range of \(-2\) to \(4\). This implies that the graph of the function will consist of discrete points corresponding to each integer within this interval. Specifically, the points will be at the following:
- \( x = -2, -1, 0, 1, 2, 3, \) and \( 4 \).
Each of these points will lie on the line defined by the equation \( y = 3x - 2 \).
In **Option 2**, the function \( y = 3x - 2 \) is defined for all real numbers of \( x \) within the range of \(-2 \leq x \leq 4\). This means the graph will be a continuous line segment that starts at \( x = -2 \) and ends at \( x = 4 \). At every point in this interval, including all the real (fractional and irrational) numbers between \(-2\) and \(4\), the function is defined and the graph will be a straight line without any breaks.
### Differences in Their Graphs:
- **Option 1 (Integer Domain):** The graph will be a series of discrete points.
- **Option 2 (Real Number Domain):** The graph will be a continuous line segment.
This distinction illustrates two key types of functions: one where the domain is restricted to specific values (like integers), resulting in a discrete graph, and another where the domain includes all values within a range, resulting in a continuous graph.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fabdd2b22-4ba6-47f3-a877-c30c59305ffe%2F2bd952fb-10e5-43ee-864c-4e0cb850609a%2Fog8irr_processed.jpeg&w=3840&q=75)
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