g Find the mean and the variance of the random variable X with probability function or density f(x) of a uniform distribution on [0, 8].

E(X) = 4

              V(X) =

Step-by-step explanation: An uniform distribution is a random variable X restricted to a finite interval [a,b] and has a constant function f(x) over this interval, i.e., the function is of form:

f(x) =  

The mean or expectation of an unifrom distribution is:

E(X) =

For the density function in interval [0,8], expectation value is:

E(X) =

E(X) =

E(X) =

E(X) =

E(X) =

E(X) = 4

Variance of a probability distribution can be written as:

V(X) =

For uniform distribution in interval [0,8]:

V(X) =

V(X) =

V(X) =

V(X) =

V(X) = - 16

V(X) =

The mean and variance are 4 and 16/3, respectively

so, converting firstly the mixed fractions to improper fractions and then "adding".