If I buy life insurance, and then die within 2 months of buying it, would family get paid?

It depends on the type of life insurance you bought and how you died.

For instance, if the cause of death was suicide it would not be covered, because suicide is excluded for 2 years, one year in Colorado.

In addition, if the life insurance plan was a graded benefit policy, the beneficiary would only receive the premiums paid, since full coverage would not be available until after the insured owned the life insurance plan for at least 2 years.

However, if the cause of death was within the coverage terms of the policy and not excluded, and the life insurance plan was a whole life insurance or term life insurance, not a graded benefit policy, the beneficiary would probably receive the death benefit.