N(t) must be greater than or equal to 0 is a property of counting processes.

N(t) must be greater than or equal to 0 is a property of counting processes.

• A. True
• B. False
• C. Sometimes
• D. Never

Answer: (A)

A counting process measures how many events have occurred by time t, so its value is always a nonnegative integer. You can’t have a negative count of events, and in most setups N(0) = 0 and N(t) only increases when events happen. Because of this inherent nonnegativity, N(t) must be greater than or equal to zero for all times. That makes the statement true. The other options would imply negative counts or ambiguity, which contradicts the basic definition of a counting process.

A counting process measures how many events have occurred by time t, so its value is always a nonnegative integer. You can’t have a negative count of events, and in most setups N(0) = 0 and N(t) only increases when events happen. Because of this inherent nonnegativity, N(t) must be greater than or equal to zero for all times. That makes the statement true. The other options would imply negative counts or ambiguity, which contradicts the basic definition of a counting process.