Answer:
The expected value of the distribution is 7.
Step-by-step explanation:
The random variable X is known to be uniformly distributed between 2 and 12.
The probability density function of X is:
[tex]f_{X}(x)=\frac{1}{b-a};\ a<X<b[/tex]
Here a = 2 and b and 12.
Compute the expected value of the distribution as follows:
[tex]E(X)=\frac{a+b}{2}[/tex]
[tex]=\frac{2+12}{2}\\\\=\frac{14}{2}\\\\=7[/tex]
Thus, the expected value of the distribution is 7.
