gaokao 2010 Q6

gaokao · China · shanghai-science Discrete Probability Distributions Probability Distribution Table Completion and Expectation Calculation

6. The probability distribution of the random variable $\xi$ is given in the table below:

$\mathbf { x }$	7	$\mathbf { 8 }$	$\mathbf { 9 }$	$\mathbf { 1 0 }$
$\mathbf { P } ( \xi = x )$	0.3	0.35	0.2	0.15

Then the expected value of the random variable $\xi$ is $\_\_\_\_$ $8.2$
Analysis: This examines the definition of expected value. $\mathrm { E } \xi = 7 \times 0.3 + 8 \times 0.35 + 9 \times 0.2 + 10 \times 0.15 = 8.2$

(5 points) As shown in the figure, a point P moves counterclockwise on a circle of radius 2. Its initial position is $P _ { 0 } ( \sqrt { 2 } , - \sqrt { 2 } )$, and its angular velocity is 1. Then the distance $d$ from point P to the $x$-axis as a function of time $t$ has a graph approximately as follows:

6. The probability distribution of the random variable $\xi$ is given in the table below:

\begin{center}
\begin{tabular}{ | c | c | c | c | c | }
\hline
$\mathbf { x }$ & 7 & $\mathbf { 8 }$ & $\mathbf { 9 }$ & $\mathbf { 1 0 }$ \\
\hline
$\mathbf { P } ( \xi = x )$ & 0.3 & 0.35 & 0.2 & 0.15 \\
\hline
\end{tabular}
\end{center}

Then the expected value of the random variable $\xi$ is $\_\_\_\_$ $8.2$

Analysis: This examines the definition of expected value. $\mathrm { E } \xi = 7 \times 0.3 + 8 \times 0.35 + 9 \times 0.2 + 10 \times 0.15 = 8.2$\\

Paper Questions

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