Mamma Temte bakes six pies a day that cost $2 each to produce. On 39% of the days she sells only two pies. On 16% of the days, she sells 4 pies, and on the remaining 45% of the days, she sells all six pies. If Mama Temte sells her pies for $6 each, what is her expected profit for a day's worth of pies? Assume that any left over pies are given away for free.