Question

5.1 basics of probability distributions. compute the mean and standard deviation of a discrete random variable.

x	p(x)
5	0.15
8	0.3
11	0.45

find the mean and standard deviation of this probability distribution.
give your answer to at least 2 decimal places.

mean (μ):

standard deviation (σ):

question help: message instructor post to forum

Explanation:

Step1: Calculate the mean formula

The mean $\mu$ of a discrete - random variable is given by $\mu=\sum_{i}x_{i}P(x_{i})$.

$$
LATEXBLOCK0
$$

Step2: Calculate the variance formula

The variance $\sigma^{2}=\sum_{i}(x_{i}-\mu)^{2}P(x_{i})$.

$$
LATEXBLOCK1
$$

Step3: Calculate the standard - deviation formula

The standard deviation $\sigma=\sqrt{\sigma^{2}}$. Since $\sigma^{2}=8.91$, then $\sigma=\sqrt{8.91}\approx2.98$.

Answer:

Mean ($\mu$): $8.30$
Standard Deviation ($\sigma$): $2.98$