Question

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

x	p(x)
0	0.15
1	0.05
2	0.05
3	0.75

find the mean (μ) of this probability distribution. round your answer to one decimal place.
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Explanation:

Step1: Recall mean formula

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

Step2: Calculate the product for each pair

For $x = 0$ and $P(0)=0.15$, $0\times0.15 = 0$.
For $x = 1$ and $P(1)=0.05$, $1\times0.05=0.05$.
For $x = 2$ and $P(2)=0.05$, $2\times0.05 = 0.1$.
For $x = 3$ and $P(3)=0.75$, $3\times0.75=2.25$.

Step3: Sum up the products

$\mu=0 + 0.05+0.1 + 2.25=2.4$.

Answer:

$2.4$