Question:
Let $X$ be a continuous random variable denoting the temperature measured.
The range of temperature is $[0, 100]$ degree Celsius and the probability density function of $X$ be $f(x) = 0.01$ for $0 \le X \le 100$.
The mean of $X$ is \(\underline{\hspace{2cm}}\)
Let $X$ be a continuous random variable denoting the temperature measured.
The range of temperature is $[0, 100]$ degree Celsius and the probability density function of $X$ be $f(x) = 0.01$ for $0 \le X \le 100$.
The mean of $X$ is \(\underline{\hspace{2cm}}\)
Show Hint
A constant PDF over an interval always represents a uniform distribution; its mean is simply the midpoint.
Updated On: Dec 30, 2025
- 2.5
- 5.0
- 25.0
- 50.0
Show Solution
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The Correct Option is D
Solution and Explanation
Step 1: Identify the PDF.
The PDF is constant:
\[
f(x) = 0.01, 0 \le x \le 100.
\]
Step 2: Compute the mean of a uniform distribution.
A constant PDF over $[0,100]$ means $X$ is uniform on $[0,100]$.
Mean of uniform distribution is:
\[
E[X] = \frac{a + b}{2} = \frac{0 + 100}{2} = 50.
\]
Step 3: Final conclusion.
Thus, the mean is:
\[
\boxed{50}
\]
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