Many random number generators allow users to specify the range of the random num

Question

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. (a) What is the height of the density curve between 0 and 2? (Enter your answer to two decimal places.) Draw a graph of the density curve. O 20468 O 95 1520 0.5 O00 5L01520 O 2 04 68 (b) Use your graph from (a) and the fact that probability is area under the curve to find pys 1.. (Enter your answer to three decimal places.) (c) Find Po.6

Explanation / Answer

a. With constant height and area of curve from y = 0 to 2 is 1 (total probability)

height = 1/2 = 0.50

Density curve: Option 3 (Bottom left, flat line at height 0.5 from Y = 0 to Y = 2)

b. P(Y <= 1.1) = (1/2) * (1.1-0) = 0.55

c. P(0.6 < Y < 1.6) = (1/2)*(1.6-0.6) = 0.50

d. P(Y >= 0.6) = (1/2)*(2-0.6) = 0.70

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