The probability density function f(x) of a random variable x that has a uniform distribution between a and b is:
-(b + a)/2
-(a − b)/2
-1/b − 1/a
-none of these choices.

The probability density function (pdf) is;

f(x)= for a ≤ x ≤ b.

while the mean is given as

And the standard deviation given as

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below: