How did the arms race contributed events in cuba and intensify the cold war

The United States and Russia were in competition with each other to build up the most nuclear weapons. With this, elevated aggression and threats brought the two countries closer and closer to full out war. Russia saw Cuba as a prime target to build missile sites for nuclear warheads as it was so close to Florida, the United States wouldn't have time to react to the nuclear strike. 

Race, for example, the chinese exclusion act