Answer:
On the outside, Gatsby is a cool and secure man. But on the inside, he is scared and insecure.
Explanation:
Jay Gatsby is the main character is F. Scott Fitzgerald's novel "The Great Gatsby", even though the story is narrated through the eyes of a different character, Nick.
As Nick gets to know Gatsby, the adjective he most often associates with the millionaire is "cool". Gatsby has this secure presence, calm, collected, polite, surrounded by mystery. He is this millionaire who came out of nowhere and took the city by storm. Everyone has a different story about him, some even accuse him of being a murderer. Still, to everyone's eyes, he is a cool man:
But young men didn’t—at least in my provincial inexperience I believed they didn’t—drift coolly out of nowhere and buy a palace on Long Island Sound. - page 54
‘Who wants to go to town?’ demanded Daisy insistently. Gatsby’s eyes floated toward her. ‘Ah,’ she cried, ‘you look so cool.’
Their eyes met, and they stared together at each other, alone in space. With an effort she glanced down at the table.
‘You always look so cool,’ she repeated. - page 126
However, Gatsby's coolness and secure sense of self is nothing but a facade. Born miserably poor, Gatsby was always an ambitious person. But he lives in a cruel world that will not simply accept him just because he is now wealthy. He is "new money", which means there is no tradition, no family name behind his wealth. He is uneducated and, as is revealed later, is indeed a criminal. He made his fortune as a bootlegger. At several moments, his insecurity is partially revealed; at a certain point, his coolness is shattered:
He looked at me sideways—and I knew why Jordan Baker had believed he was lying. He hurried the phrase ‘educated at Oxford,’ or swallowed it or choked on it as though it had bothered him before. And with this doubt his whole statement fell to pieces and I wondered if there wasn’t something a little sinister about him after all. - page 70; Gatsby is trying to convince Nick of his "true" history as an Oxford man.
Then I turned back to Gatsby—and was startled at his expression. He looked—and this is said in all contempt for the babbled slander of his garden—as if he had ‘killed a man.’ For a moment the set of his face could be described in just that fantastic way - page 143; when Tom confronts Gatsby about his "business".