Question

A continuous random variable X is uniformly distributed with 0less than or equals Xless than or equals25 .

​(a) Draw a graph of the uniform density function.

​(b) What is ​P(0 less than or equalsXless than or equals8 ​)?

​(c) What is ​P(13 less than or equalsXless than or equals15​)

Answer 1

To draw the graph of the uniform density function for a continuous random variable X, calculate the probabilities P(0 ≤ X ≤ 8) and P(13 ≤ X ≤ 15), divide the respective intervals by the length of the entire interval [0, 25].

Step-by-step explanation:

To draw the graph of the uniform density function for a continuous random variable X uniformly distributed between 0 and 25, we draw a rectangle with the horizontal sides at 0 and 25 and the vertical sides at 0 and the height of the probability density function.

(b) To calculate the probability P(0 ≤ X ≤ 8), we divide the length of the interval [0, 8] by the length of the entire interval [0, 25]. This gives us a probability of 8/25 or 0.32.

(c) To calculate the probability P(13 ≤ X ≤ 15), we again divide the length of the interval [13, 15] by the length of the entire interval [0, 25]. This gives us a probability of 2/25 or 0.08.