Aquantity x has cumulative distribution function p(x) = x − x2/4 for 0 ≤ x ≤ 2 and p(x) = 0 for x < 0 and p(x) = 1 for x > 2. find the mean and median of x.

The mean of x is 2/3, and the median of x is

The cumulative distribution function is given as:

Differentiate the cumulative distribution function.

So, we have:

The mean is then calculated as:

So, we have:

Expand

Integrate

Expand

Reduce fraction

So, the mean of x is 2/3

To calculate the median, we have:

Rewrite as:

The median element at the mid-position (i.e. 1/2).

So, we have:

Multiply through by 4

Rewrite as:

Solve for M

Recall that:

The domain is given as:

is outside the domain.

Hence, the median of x is

Read more about mean and median at:

link

hope it you

step-by-step explanation:

sin(7pi/6 - pi/3)  

= sin(7pi/6 - 2pi/6)  

= sin(5pi/6)  

= sin(pi - pi/6)  

= sin(pi/6)  

= 1/2  

sin 7pi/6 - sin pi/3  

= sin (pi + pi/6) - sin pi/3  

= -sin pi/6 - sin pi/3  

= -1/2 - sqrt(3)/2  

= -(1+sqrt(3))2

answer: 100

step-by-step explanation: