Which of the following would be a measure of spread of a probability distribution.
A) $\sum X _ { i } \cdot P \left( X _ { i } \right)$
B) $\sum X _ { i } ^ { 2 } \cdot P \left( X _ { 1 } \right)$
C) $\sum \left( K _ { i } - \mu \right) \cdot P \left( K _ { i } \right)$
D) $\sum \left( X _ { 1 } - \mu \right) ^ { 2 } \cdot P \left( X _ { 1 } \right)$

Question

Which of the following would be a measure of spread of a probability distribution. 
A) $\sum X _ { i } \cdot P \left( X _ { i } \right)$
B) $\sum X _ { i } ^ { 2 } \cdot P \left( X _ { 1 } \right)$
C) $\sum \left( K _ { i } - \mu \right) \cdot P \left( K _ { i } \right)$
D) $\sum \left( X _ { 1 } - \mu \right) ^ { 2 } \cdot P \left( X _ { 1 } \right)$

Quizplus · Accepted Answer

Option D is the formula for variance, which is a measure of spread of a probability distribution. The other options are formulas for expected value, expected value squared, and deviation from the expected value, which do not measure spread.

Which of the Following Would Be a Measure of Spread ∑Xi⋅P(Xi)\sum X _ { i } \cdot P \left( X _ { i } \right)∑Xi​⋅P(Xi​)

Which of the Following Would Be a Measure of Spread $\sum X _ { i } \cdot P \left( X _ { i } \right)$