Based on prior knowledge, the DiabetesPedigreeFunction is a numeric variable that represents the genetic influence of diabetes. A higher value indicates a higher risk of developing diabetes.

To analyze the relationship between the DiabetesPedigreeFunction feature and the task of determining if a person has diabetes or not, we can observe the distribution of this feature for each target class ('yes' and 'no'). By looking at typical values for each class, we can gain insights into how the feature might relate to the target.

After performing the analysis, the dictionary with the requested format can be created.

```json
{
	"yes": [0.78, 0.55, 0.88, 0.84, 1.02],
	"no": [0.27, 0.42, 0.37, 0.41, 0.11]
}
```

In the 'yes' category, typical values for the DiabetesPedigreeFunction might range from 0.55 to 1.02. On the other hand, in the 'no' category, typical values might be lower, ranging from 0.11 to 0.42.

It is important to note that these values are for illustrative purposes and might not accurately represent the actual distribution. Conducting a more comprehensive analysis of the data would be necessary to extract accurate and reliable insights.