Question

For a random variable X, if  V( X ) = 0.1, then the probability of the event: (X - E(X) )² > 10,

A) Cannot be greater than 0.

B) Cannot be greater than 0.01

C) Cannot be greater than 0.001

D) None of the above

Answer 1

The probability required here is computed as:
P( [X - E(X)]² ) > 10

Due to symmetry about 0, this can be written as:

Converting to a standard normal variable, we have here:

This is approximately equal to 0 but slightly greater than 0.

Theefore cannot be greater than 0.001 is the correct answer here. because it is slightly greater than 0 but less than 0.001 here.