Let X be a continuous random variable denoting the temperature measured. The range of temperature is [0, 100] degree Cel...

Question

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 ________

A. 2.5
B. 5.0
C. 25.0
D. 50.0

Accepted Answer

Mean of X = 50.0 (Option D) When a continuous random variable is uniformly distributed over an interval, every temperature in that range is equally likely. The probability density function is a constant, and the mean is simply the midpoint of the interval. Here the interval is [0, 100], so the mean is the centre, which is 50.

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 ________ A. 2.5 B. 5.0 C. 25.0 D. 50.0