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 4. Call the random number generated Y. Then the density curve of the random variable Y has constant height between 0 and 4, and height 0 elsewhere.

(a) What is the height of the density curve between 0 and 4? (Enter your answer to two decimal places.)

Which is the graph of the density curve?

(b) Use your graph from (a) and the fact that probability is area under the curve to find

P(Y 1.5).

(Enter your answer to three decimal places.)

(c) Find

P(0.2 < Y < 1.8).

(Enter your answer to three decimal places.)

(d) Find

P(Y 0.8).

(Enter your answer to three decimal places.)

Explanation / Answer

a) The height of the graph = 1/(4-0) =1/4 = 0.25

The graph distributed uniformly between 0 to 4 , so 2nd grapg is correct

b) P(Y 1.5) = (1.5 -0) /4 =0.375

c) P(0.2 < Y < 1.8) = (1.8 - 0.2)/ 4 = 0.4

d) P(Y 0.8) = (4- 0.8) /4 = 0.8

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