X 4 6 9 11 15
P(x) 0.20 0.34 0.15 0.22 0.09
This table shows a probability
distribution for a discrete random
variable. What is the mean of this
discrete random variable?
O9
O 0.2
0 1
O 7.96

The mean of this  discrete random variable is 7.96

Solution:

Given that,

x         4       6          9         11        15

P(x)   0.20   0.34     0.15    0.22     0.09

Mean is given as:

Therefore,

Thus, mean of this  discrete random variable is 7.96

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: