Step 2: What is the height of the density curve between 0 and 2? Draw a graph of

Question

Step 2:
What is the height of the density curve between 0 and 2? Draw a graph of the density curve.

Step 3:
Use your graph of the density curve and the fact that probability is area under the curve to find P(Y ? 1).

(12.51) Many random number generators allow users to specify the range of the random numbers to be produced. Suppose that you specify that the random number Y can take any value between 0 and 2. Then the density curve of the outcomes has constant height between 0 and 2, and height 0 elsewhere.

Step 1:
Is the random variable Y discrete or continuous? Why? Discrete, because we do not know the number that will be chosen. Discrete, because the sample space {0, 2} is finite. Continuous, because the length of the interval is finite. Continuous, because there is an infinite number of values in the interval.

Step 2:
What is the height of the density curve between 0 and 2? Draw a graph of the density curve.

Step 3:
Use your graph of the density curve and the fact that probability is area under the curve to find P(Y ? 1).

Explanation / Answer

Answer - D Continuous, because there is an infinite number of values in the interval

B. Basic is the area under the curve is always 1.
Height is 1/2.

The density function p(y)=c*(1/2) with the normalization that p(y)dy from 0 to 2 =1 so c=1 and p(y)=1/2 for 0y2 and 0 for y>2.

So P(.5<y<1.3)= .51.3p(y)dy=(1/2)*(1.3-.5)=.4

and P(y1.2)=1.2 p(y)dy=(1/2)*(2-1.2)=.4

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