Question

For the given distribution X∼U(0,12)X∼U(0,12), what is the theoretical standard deviation?

A) 22
B) 33
C) 44
D) 66

Answer 1

The theoretical standard deviation of a uniform distribution X ~ U(0, 12) is calculated with the formula √((12 - 0)² / 12), which approximately equals 3.46.

Step-by-step explanation:

The question asks for the theoretical standard deviation of a uniform distribution defined by X ~ U(0, 12). The notation U(a, b) indicates that X follows a uniform distribution with minimum value a and maximum value b. For a uniform distribution U(a, b), the theoretical standard deviation is calculated using the formula √((b - a)² / 12). Applying this formula to our distribution:

• a = 0
• b = 12

Therefore, the theoretical standard deviation of X ~ U(0, 12) is:

√((12 - 0)² / 12) = √(144 / 12) = √12 = 3.46 (approx.)

None of the answer options listed matches the correct value, but if we need to choose the closest one, option B) 3 would be the nearest correct answer, given that in an actual question, answer options would be rounded values.