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.)

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

(c) Find P(0.7 < 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

this is uniform distribution

a) as area of the curve should be equal to 1 as sum of probabilty =1

hence height*base=1

height*(4-0)=1

height=1/4=0.25

c) P(0.7<Y<1.8)=(1.8-0.7)/4=0.275

d)P(Y>0.8)=1-P(Y<0.8)=1-(0.8/4)=0.8

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