For each one of the following figures, identify if it is a valid CDF. The value of the CDF at points of discontinuity is indicated with a small solid circle.
(original images belonging to: "The science of uncertainty")
1. No, it is not a valid CDF
2. Yes, it is not a valid CDF
3.No, it is not a valid CDF
4.No, it is not a valid CDF
No,No,Yes,No
Well, it seems like none of them made the cut as valid CDFs. They wouldn't even pass the "CDF Appreciation Society" membership application! Keep on searching, I'm sure there's a valid CDF out there just waiting to be found.
To determine if each figure is a valid cumulative distribution function (CDF), we need to check if it satisfies the properties of a CDF.
1. Figure 1: No, it is not a valid CDF. A valid CDF should be non-decreasing, but in this figure, the graph decreases from point B to point C, violating this property.
2. Figure 2: Yes, it is not a valid CDF. This statement seems contradictory. If it is not a valid CDF, then it cannot be classified as "Yes". Please double-check the statement.
3. Figure 3: No, it is not a valid CDF. The function should be non-decreasing, but in this figure, the graph shows a jump from point A to point B, violating this property.
4. Figure 4: No, it is not a valid CDF. A valid CDF should start at 0 and end at 1, but in this figure, the graph starts at a nonzero value and does not reach 1, violating these properties.
Please note that the correct answers may vary depending on the specific properties being violated in each figure.
To determine whether each figure is a valid cumulative distribution function (CDF), we need to check if it satisfies three main conditions:
1. Non-negative values: The CDF must have non-negative values throughout the distribution.
2. Monotonicity: The CDF must be a non-decreasing function, meaning that as the value of the random variable increases, the cumulative probability also increases.
3. Limits: The CDF must approach 0 as the random variable goes to negative infinity and approach 1 as the random variable goes to positive infinity.
Now, let's analyze each figure:
1. Since the first figure has a discontinuity where the value of the CDF jumps from 0.4 to 0.6, it violates the monotonicity property. Consequently, it is not a valid CDF.
2. The second figure does not have any discontinuities, and it satisfies the non-negativity condition. However, as we can see from the graph, the CDF does not approach 1 as the random variable goes to positive infinity. Therefore, it does not satisfy the limit condition and is not a valid CDF.
3. The third figure has a discontinuity at approximately 0.5, where the value of the CDF jumps from 0.3 to 0.7. This violates the monotonicity property, making it not a valid CDF.
4. Similar to the previous figure, the fourth figure has a discontinuity where the value of the CDF jumps from 0.2 to 0.6. Thus, it also violates the monotonicity property and is not a valid CDF.
In summary, none of the provided figures represent valid cumulative distribution functions (CDFs) due to violations of either monotonicity or limit conditions.