Part 2 Assume that the probability density function is f(x) = 2.0 for an interval of length 0.5 meters. Over what value should the density be centered to achieve the greatest proportion of rods within specifications? i

Suppose we have a uniform density curve whose length is 2, what would the height of the density curve have to be? Write your answer in decimal form.

A random phenomenon results in a number in the range of 1 to 5. All values in the range are equally likely, so the density curve is flat, as shown below. What must y be such that the probability of a number between 1 and y is 25%? Please provide an explanation for your choice.

"Medians, etc problem."   Suppose X has density x−2 for x ≥ 1. Find the density function for Y = X2.

Answer both parts of the question. Show all work.

Assume that the variable under consideration has a density curve. The area under the density curve that lies to the right of 20 is 0.368.   a. What percentage of all possible observations of the variable exceed 20​?   b. What percentage of all possible observations of the variable are at most 20​?   a. ___________% ​(Type an integer or a​ decimal.)   b. ___________% ​(Type an integer or a​ decimal.)