Conditions for which the density function of a mixture of two normal distributions is bimodal are investigated. For fixed values of the variances σ1 2 and σ2 2 of the normal distributions if the difference between the means is sufficiently small, the distribution of the mixture will be unimodal, independent of the proportions p and 1 – p, 0 < p < 1. If the difference exceeds a critical value which depends on σ1 2 and σ2 2 the bimodality property then depends on p. Values of p sufficiently close to zero and one always exist for which the distribution is unimodal.
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I. Eisenberger (1964) studied this question.