This article studies the remote state estimation problem of linear time-invariant systems with stochastic event-triggered sensor schedules in the presence of packet drops between the sensor and the estimator. Due to the existence of packet drops, the Gaussianity at the estimator side no longer holds. It is proved that the system state conditioned on the available information at the estimator side is Gaussian mixture distributed. The minimum-mean-square-error (MMSE) estimator can be obtained from the bank of Kalman filters. Since the optimal estimators require exponentially increasing computation and memory with time, suboptimal estimators to reduce computational complexities by limiting the length and numbers of hypotheses are further provided. In the end, simulations are conducted to illustrate the performance of the optimal and suboptimal estimators.