This paper investigates a Bivariate mixture of the student’s t and Normal distributions, referred to as the t-Normal distribution, where the marginals are univariate Student’s t and Normal distributions, respectively. The study derives the conditional distributions along with their associated constants. It also presents several generating functions, including the moment, cumulant, characteristic, hazard, survival, cumulative hazard functions, and Shannon’s differential entropy. Three-dimensional probability surfaces illustrate the shape of the t-Normal density. Special cases of this distribution include mixtures involving logarithmic, logit, and hyperbolic sine transformations. Furthermore, the paper derives the maximum likelihood estimators for the parameters, calculates the elements of the Fisher Information matrix and explores parameter estimation through a nonlinear programming approach.