  We consider upper exponential bounds for the probability of the event that an
absolute deviation of sample mean from mathematical expectation p is bigger
comparing with some ordered level epsilon. These bounds include 2 coefficients
{alpha, beta}. In order to optimize the bound we are interested to minimize
linear coefficient alpha and to maximize exponential coefficient beta.
Generally, the value of linear coefficient alpha may not be smaller than one.
The following 2 settings were proved: 1) {1, 2} in the case of classical
discreet problem as it was formulated by Bernoulli in the 17th century, and 2)
{1, 2/(1+epsilon^2)} in the general discreet case with arbitrary rational p and
epsilon. The second setting represents a new structure of the exponential bound
which may be extended to continuous case.
