For the next 5 problems: A company making candles guarantees their candles will last at least 2 hours, just to be safe. Prior research done by the company shows the candles can actually last from 2 up to 12 hours. Let X represent the lifetime of a candle made by this company. Assume X has a uniform distribution over [2, 12].

A. Find median wait time using integration. Use the following hint: The median is the value of X where 50% of the area lies below X. This means you know the integral is equal to .50 and your job is to find the upper limit of the integral. You know the lower limit is 2.

B. Suppose X has a uniform distribution over [0, 4]. Find f(x).