please leave a brief explanation on how to find the area under the curve. Many r

Question

please leave a brief explanation on how to find the area under the curve.

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.) Draw a graph of the density curve 0 0.2 040.0. 0.2 0.4 0.6 0.8 0 (b) Use your graph from (a) and the fact that probability is area under the curve to find P(Y 1.7). (Enter your answer to three decimal places.)

Explanation / Answer

a) as we know that area under probability curve =1

here area of rectangle =1

height *base =1

height *(4-0)=1

height =1/4 =0.25

(for graph: here as height is constant and varible can take any values from0 to 4 therefore first option (ltop left most rectangle is right choice)

c) P(0.6<Y<1.7) =height*base =0.25*(1.7-0.6)=0.275

d) P(Y>=0.7) =height*base =0.25*(4-0.7)=0.825

( here probability disribution being uniform ; area under the curve =height*range of value for whcih probability is to be calculated)

please revert for any explanation required.

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