Write a Python function `is_product_even(arr)` that determines whether the product of all numbers in a given list is even. The function should return `True` if the product is even, and `False` otherwise.
#### Example Usage
```python [main.nopy]
print(is_product_even([1, 2, 3])) # Output: True
print(is_product_even([1, 1, 1])) # Output: False
print(is_product_even([2, 4, 6])) # Output: True
```
#### Constraints
- The input list will contain integers.
- The list can be empty, in which case the function should return `False` (as there are no numbers to multiply).