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Conditions for bimodality of mixtures of two unimodal distributions are investigated in some special cases. Based on general characterizations, explicit criteria for the parameters are derived for mixtures of two Cauchy, logistic, Student, gamma, log-normal, Gumbel and other distributions.

We deal with real weakly stationary processes $\{X_t,t\in \mathbb{Z}\}$ with non-positive autocorrelations $\left\{r_k\right\}$, i. e. it is assumed that $r_k\le 0$ for all $k=1,2,\cdots$. We show that such processes have some special interesting properties. In particular, it is shown that each such a process can be represented as a linear process. Sufficient conditions under which the resulting process satisfies $r_k\le 0$ for all $k=1,2,\cdots$ are provided as well.