Probability Question

Question

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

P(0.5<Y<1.3)

P(Y≥1.2).

Please show steps.

Answer 1

Hi Vivian,

 

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 0≤y≤2 and 0 for y>2.

 

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

 

and P(y≥1.2)=∫_1.2^∞ p(y)dy=(1/2)*(2-1.2)=.4

 

Regards

Jim