diff --git a/content/Exercise_set_1.md b/content/Exercise_set_1.md index 4af1a047c48290df6856981c302cf71de79cf3e9..2aab3ce0d981634a3a4c1acee3a8f457017869e5 100644 --- a/content/Exercise_set_1.md +++ b/content/Exercise_set_1.md @@ -112,7 +112,7 @@ mechanism, or multiple levels). A probability density function should be normalized: $$ - \int \limits_{-\infty}^{\infty} P(x) dx = 1. + \int \limits_{-\infty}^{\infty} P(x) \,\mathrm{d}x = 1. $$ (eq:pdf_normalized) For simplicity we consider a probability density function of a single stochastic variable @@ -122,7 +122,7 @@ generalized to multiple variables and discrete sets. The $n^{\mathrm{th}}$ moment of this distribution is defined as $$ - \langle x^n \rangle \equiv \int \limits_{-\infty}^{\infty} x^n P(x) dx. + \langle x^n \rangle \equiv \int \limits_{-\infty}^{\infty} x^n P(x) \,\mathrm{d}x. $$ (eq:moments) The first and second moment are particularly useful, and yield the mean