Let X be a continuous random variable denoting the temperature measured. The range of temperature is [0, 100] degree Celsius and let the probability density function of X be f(x) = 0.01 for 0 ≤ X ≤ 100. The mean of X is ______
Options:
(A) 2.5
(B) 5.0
(C) 25.0
(D) 50.0
Official Answer Key:
D
Step-by-Step Solution & Explanation
f(x) = 0.01 = 1/100 over [0,100] is a uniform distribution. For a uniform distribution on [a,b], mean = (a+b)/2 = (0+100)/2 = 50.0, matching (D).
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