Question

Let $ X $ be a continuous random variable denoting the temperature measured. The range of temperature is $ [0, 100] $ degrees Celsius and let the probability density function of $ X $ be $ f(X) = 0.01 $ for $ 0 \leq X \leq 100 $. The mean is

• A. 5.0
• B.
• C. 5
• D. 25.0

Hint:

For a uniform distribution, the mean is simply the average of the lower and upper bounds of the distribution.

Answer 1

The Correct Option is D

The probability density function \( f(X) = 0.01 \) represents a uniform distribution over the interval \( [0, 100] \). The mean of a uniform distribution is given by: \[ \text{Mean} = \frac{a + b}{2} \] Where \( a = 0 \) and \( b = 100 \). Therefore: \[ \text{Mean} = \frac{0 + 100}{2} = 50 \]
Thus, the correct answer is 4. 50.0.