4.59 Uniform numbers between 0 and 2. Many random number generators allow users to specify the range of the random numbers to be produced. Suppose that you specify that the range is to be all numbers between 0 and 2. Call the random number generated Y. Then the density curve of the random variable Y has constant height between 0 and 2, and height 0 elsewhere.

1. (a) What is the height of the density curve between 0 and 2? Draw a graph of the density curve.

2. (b) Use your graph from part (a) and the fact that probability is area under the curve to find P(Y ≤ 1.6).

3. (c) Find P(0.5 < Y < 1.7).

4. (d) Find P(Y ≥ 0.95).