{In this paper we define $f-\alpha\beta$-statistical convergence of order $\gamma$ in probability and $f-\alpha\beta$-strong $p$-Ces$\grave{\mbox{a}}$ro summability of order $\gamma$ in probability for a sequence of random variables under unbounded modulus function and examine the relation between these two concepts. We show by an example that this notion of $f-\alpha\beta$-statistical convergence of order $\gamma$ in probability is stronger than $\alpha\beta$-statistical convergence of order $\gamma$ in probability \cite{pd}.}