Results

Thesis & Dissertations

Theoretical and Computational Studies of Determining the Distribution and Expectation of Functions of n Continuous Random Variables

Abstract

The distribution of the minimum and maximum of a set of n independent distributed random variables has always been the interest in many areas of Science. The study of these random variables and the problem of determining their probability density functions and their expected values were inspected by many mathematicians for decades. Some problems were solved and other problems were examined, but many still need to be considered and worked on. In our work, we considered some of these problems. Our objective was to determine theoretically a closed expression of the probability density functions and the expected values of the minimum and maximum of different types of distributed random variables. The problem was solved completely for the minimum and maximum of a set of n identical uniformly distributed random variables, a set of n exponentially distributed random variables with different parameters, in addition to a set of n identical normally distributed random variables. Moreover, we analyzed numerically, by simulation, the expected values of the minimum and maximum of the sets of two and three independent identical uniformly distributed random variables, the sets of two and three independent exponentially distributed random variables with different parameters, and the sets of two and three independent identical normally distributed random variables.

Student(s)

Silvana Omar EL Rabih

Supervisor(s)

Noura Mohammad Yassein