exercise 1.the probabilities of laptops to have 0, 1, 2, 3 or 4 defective parts are 0.24, 0.18, 0.26, 0.12 and 0.20, respectively. find the mean of the probability distribution.

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Accepted Answer

## Step1: Recall the formula for the mean of a probability distribution
The formula for the mean $\mu$ of a discrete probability distribution is $\mu=\sum_{i}x_ip_i$, where $x_i$ are the values of the random variable and $p_i$ are their corresponding probabilities.
## Step2: Calculate each $x_ip_i$ term
- For $x = 0$ and $p=0.24$: $0\times0.24 = 0$
- For $x = 1$ and $p = 0.18$: $1\times0.18=0.18$
- For $x = 2$ and $p = 0.26$: $2\times0.26 = 0.52$
- For $x = 3$ and $p = 0.12$: $3\times0.12=0.36$
- For $x = 4$ and $p = 0.20$: $4\times0.20 = 0.8$
## Step3: Sum up the $x_ip_i$ terms
$\mu=0 + 0.18+0.52 + 0.36+0.8$
$$
\begin{align*}
\mu&=(0.18 + 0.52)+(0.36 + 0.8)\
&=0.7+1.16\
&=1.86
\end{align*}
$$

# Answer:
$1.86$

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QUESTION IMAGE

Question

Explanation:

Step1: Recall the formula for the mean of a probability distribution

Step2: Calculate each \(x_ip_i\) term

Step3: Sum up the \(x_ip_i\) terms

Answer: