Thank you all for quick responses
I was trapped in thinking that the probability theory (being rigorous) should be 3rd or 4th year course.
Based on the concepts mentioned above, I think the closest one that matches is "Introduction to Statistics II", which is a 2nd year course.
Course description goes:
This course provides students with an introduction to statistical methods with an emphasis on applications using continuous probability models.
This course serves as an introduction to mathematical statistics, and is devoted to the study of the basic probability tools needed in the theory of statistical inference. Topics include joint distributions, multivariate change of variables formula, conditional and marginal distributions, conditional expectation, covariance and correlation, and moment generating functions. Distributional results including those associated with normally distributed observations are examined. In addition, this course considers maximum likelihood and Bayesian estimation (time permitting). The topics considered in this course require knowledge of univariate and multivariate calculus.