If two variables having the same mean and variance, then can we drop one variable and take the another.
It’s not clear what you mean with “can” here. My instinct is to say that it depends on what you’re trying to accomplish and how.
For now, I will stick with “you cannot do this indiscriminately”. Here’s a fairly simple example. In the table below we have three columns: two features and a target variable.
| Col1 | Col2 | Target | |------|------|--------| | 1 | 0 | 1 | | 0 | 1 | 1 | | 1 | 1 | 2 |
The features clearly have the same mean and variance — I say clearly because they have the same number of 1s.
The target variable is simply the sum of the features, but pretend you don’t know this and drop one of the features. Then you’d be losing predictive power.