What does the variance of a random variable measure? What is the standard deviation of a continuous random variable X?

Tabansi

Tabansi

Answered question

2020-10-21

What does the variance of a random variable measure?
What is the standard deviation of a continuous random variable X?

Answer & Explanation

saiyansruleA

saiyansruleA

Skilled2020-10-22Added 110 answers

Step 1 
A random variable's variance quantifies how widely distributed a set of (random) integers are relative to their mean.
Step 2 
A random variable with an unlimited number of possible values is said to be continuous. Any value between the ranges of values is possible for the continuous random variable. The mean deviation of the random variable from the mean value is known as the standard deviation of any variable. It establishes how the data values are distributed around the mean.

A variable's distribution will be closer to the mean value if the standard deviation is less. A variable's distribution will be further from the mean value if the standard deviation is higher.
The following is the definition of the formula for the continuous random variable X's standard deviation:
σ=(xμ)2f(x) dx 

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