use the probability distribution for the random variable $x$ to answer the question.

\
\begin{array}{c|cccccc}
x & 0 & 1 & 2 & 3 & 4 & 5 \\
\hline
p(x) & 0.2 & 0.25 & 0.05 & 0.3 & 0.05 & 0.15
\end{array}
\

find $\mu$, $\sigma^2$, and $\sigma$. (round your standard deviation to two decimal places.)

$\mu = $
$\sigma^2 = $
$\sigma = $

Question

use the probability distribution for the random variable $x$ to answer the question.

\
\begin{array}{c|cccccc}
x & 0 & 1 & 2 & 3 & 4 & 5 \\
\hline
p(x) & 0.2 & 0.25 & 0.05 & 0.3 & 0.05 & 0.15
\end{array}
\

find $\mu$, $\sigma^2$, and $\sigma$. (round your standard deviation to two decimal places.)

$\mu = $
$\sigma^2 = $
$\sigma = $

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Discrete Random Variables", "Variance of Discrete Random Variable", "Standard Deviation of Discrete Random Variable" ], "new_concepts": [], "current_concepts": [ "Discrete Random Variables", "Variance of Discrete Random Variable", "Standard Deviation of Discrete Random Variable" ] } ## Calculate the expected value Using the *Discrete Random Variables* knowledge point $$ \begin{aligned} \mu = E(X) &= \sum x \cdot p(x) \ &= 0(0.2) + 1(0.25) + 2(0.05) + 3(0.3) + 4(0.05) + 5(0.15) \ &= 0 + 0.25 + 0.10 + 0.90 + 0.20 + 0.75 \ &= 2.20 \end{aligned} $$ ## Calculate the variance Using the *Variance of Discrete Random Variable* knowledge point $$ \begin{aligned} E(X^2) &= \sum x^2 \cdot p(x) \ &= 0^2(0.2) + 1^2(0.25) + 2^2(0.05) + 3^2(0.3) + 4^2(0.05) + 5^2(0.15) \ &= 0 + 0.25 + 0.20 + 2.70 + 0.80 + 3.75 \ &= 7.70 \ \sigma^2 &= E(X^2) - \mu^2 \ &= 7.70 - (2.20)^2 \ &= 7.70 - 4.84 \ &= 2.86 \end{aligned} $$ ## Calculate the standard deviation Using the *Standard Deviation of Discrete Random Variable* knowledge point $$ \begin{aligned} \sigma &= \sqrt{\sigma^2} \ &= \sqrt{2.86} \ &\approx 1.6912 \approx 1.69 \end{aligned} $$ Use the probability distribution for the random variable $x$ to answer the question. | $x$ | 0 | 1 | 2 | 3 | 4 | 5 | | :--- | :--- | :--- | :--- | :--- | :--- | :--- | | $p(x)$ | 0.2 | 0.25 | 0.05 | 0.3 | 0.05 | 0.15 | Find $\mu$, $\sigma^2$, and $\sigma$. (Round your standard deviation to two decimal places.) $\mu =$ 2.2 $\sigma^2 =$ 2.86 $\sigma =$ 1.69 { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Statistics", "Discrete Random Variables" ] }

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QUESTION IMAGE

Question

Explanation:

Calculate the expected value

Calculate the variance

Calculate the standard deviation

Answer: