Using an effective field theory based on the use of a probability distribution technique that accounts for the self-spin-correlation function, a ferrimagnetic mixed spin-1 and spin-3/2 Blume-Capel model in a random longitudinal field is investigated. The existence and dependence of a compensation point on the random field and on the anisotropy strength is investigated. A tricritical behavior is observed for given values of the parameters of the system.