Find the mean of the random variable x associated with the probability density function over the indicated interval. ;
A)
B)
D)
E)

Question

Find the mean of the random variable x associated with the probability density function over the indicated interval. ​  ;  ​
A) ​ 
B) ​ 
D) ​ 
E) ​

Quizplus · Accepted Answer

To find the mean of the random variable x, we need to find the expected value of x over the given interval, which is given by the formula:

E(x) = ∫x*f(x) dx

where f(x) is the probability density function.

In this case, the probability density function is:

f(x) = (3/4)*(x - 1), for 1 ≤ x ≤ 2
      0,           otherwise

So, we have:

E(x) = ∫1^2 x*(3/4)*(x - 1) dx
     = (3/4) ∫1^2 (x^2 - x) dx
     = (3/4) [(1/3)*2^3 - (1/2)*2^2 - (1/3)*1^3 + (1/2)*1^2]
     = (3/4) [(8/3) - 2/2 - (1/3) + 1/2]
     = (3/4) [(5/3)]
     = 5/4

Therefore, the mean of the random variable x is 5/4, which is option C.

Find the Mean of the Random Variable X Associated with the Probability