Statement-I: Correct - The troposphere is thicker at the equator than at the poles. This is because the equator receives more direct sunlight, leading to warmer temperatures and greater air expansion. This expanded air results in a greater height of the troposphere.

Statement-II: Correct - Convection is a significant mode of heat transfer in the atmosphere. At the equator, intense solar heating causes air to rise rapidly in strong convectional currents. This rising air carries heat to higher altitudes, contributing to the vertical distribution of heat in the troposphere.

Statement II directly explains Statement I. The strong convectional currents mentioned in Statement II are the primary reason for the greater thickness of the troposphere at the equator, as explained in Statement I. The rising air due to convection leads to the expansion and increased height of the troposphere in equatorial regions.