Question

question 14 5.1 basics of probability distributions. compute the mean and standard deviation of a discrete random variable. x p(x) 0 0.15 1 0.3 2 0.05 3 0.5 find the mean (μ) of this probability distribution. round your answer to one decimal place.

Explanation:

Step1: Recall mean formula

The mean $\mu$ of a discrete - random variable is given by $\mu=\sum x\cdot P(x)$.

Step2: Calculate each product

For $x = 0$ and $P(0)=0.15$, the product is $0\times0.15 = 0$.
For $x = 1$ and $P(1)=0.3$, the product is $1\times0.3=0.3$.
For $x = 2$ and $P(2)=0.05$, the product is $2\times0.05 = 0.1$.
For $x = 3$ and $P(3)=0.5$, the product is $3\times0.5=1.5$.

Step3: Sum up the products

$\mu=0 + 0.3+0.1 + 1.5=1.9$

Answer:

$1.9$