Question

Find the density function of a normally distributed random variable X, if E(X) = 7.8 and σ(X) = 4.1

Answer 1

Answer on Question #43529-Math-Statistics and Probability

Find the density function of a normally distributed random variable $X$, if $E(X) = 7.8$ and $\sigma(X) = 4.1$.

Solution

The density function of a normally distributed random variable $X$ is

$$f(x) = \frac{1}{\sigma\sqrt{2\pi}} e^{-\frac{(x-\mu)^2}{2\sigma^2}} = \frac{1}{4.1\sqrt{2\pi}} e^{-\frac{(x-7.8)^2}{2 \cdot 4.1^2}} = 0.0973 \cdot e^{-\frac{(x-7.8)^2}{33.62}}.$$

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