A spinner from a board game randomly indicates a real number between 0 and $10 .$ The spinner is fair in the sense that it indicates a number in a given interval with the same probability as it indicates a number in any other interval of the same length. (a) Explain why the function $$ f(x)=\left\{\begin{array}{ll} 0.1 & \text { if } 0 \leqslant x \leqslant 10 \\ 0 & \text { if } x<0 \text { or } x>10 \end{array}\right. $$ is a probability density function for the spinner's values. (b) What does your intuition tell you about the value of the mean? Check your guess by evaluating an integral.
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(a) To show that $f(x)$ is a probability density function, we need to verify two conditions: Show more…
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A spinner from a board game randomly indicates a real number between 0 and $10 .$ The spinner is fair in the sense that it indicates a number in a given interval with the same probability as it indicates a number in any other interval of the same length. \begin{equation} \begin{array}{l}{\text { (a) Explain why the function }} \end{array} \end{equation} $$f(x)=\left\{\begin{array}{ll}{0.1} & {\text { if } 0 \leqslant x \leqslant 10} \\ {0} & {\text { if } x<0 \text { or } x>10}\end{array}\right.$$ \begin{equation} \begin{array}{l}{\text { is a probability density function for the spinner's values. }} \\ {\text { (b) What does your intuition tell you about the value of the }} \\ {\text { mean? Check your guess by evaluating an integral. }}\end{array} \end{equation}
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A spinner from a board game randomly indicates a real number between 0 and $10 .$ The spinner is fair in the sense that it indicates a number in a given interval with the same probability as it indicates a number in any other interval of the same length. (a) Explain why the function $f(x)=\left\{\begin{array}{ll}{0.1} & {\text { if } 0 \leqslant x \leqslant 10} \\ {0} & {\text { if } x<0 \text { or } x>10}\end{array}\right.$ is a probability density function for the spinner's values. (b) What does your intuition tell you about the value of the mean? Check your guess by evaluating an integral.
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