Question

Suppose that X ∼ U(-1.1, 5.5). Find the standard deviation of X

Round your answer to the nearest ten thousandth.

Answer 1

Solution:

Given data:

The distribution is X $\sim$ U(-1.1, 5.5)

Now, we have to find out the :

Standard deviation of X :

X $\sim$ U(-1.1, 5.5) distribution is the uniform distribution.

The uniform distribution is X $\sim$ U(a,b)

We already know the formula of  standard deviation .i.e.,

Standard deviation of X =  $\sqrt{\frac{1}{12}(b-a)^{2}}$

= $\sqrt{\frac{1}{12}(5.5-(-1.1))^{2}}$

=   $\sqrt{\frac{1}{12}(5.5+1.1)^{2}}$

=   $\sqrt{\frac{1}{12}(6.6)^{2}}$

   = $\sqrt{\frac{1}{12}(43.56)}$

=    $\sqrt{3.63}$

   = 1.905

$\therefore$ Standard deviation of X  = 1.905 $\sim$2