Probability of Continuous Variables

[Naseer Asif]

If x belongs to [1,3] and y belongs to [1,4], find the probability that x<y.

Can anyone solve it…

[acd]

Well, you need the joint density of the 2 variables. Then, draw the domain D={X<Y; 0<X<3; 0<Y<4} in the XY plane, and your probability is just the double integral of the joint density over D. For instance, if X and Y are uniformly distributed and independent, the probability is the area of D.
Hope this helps.

[Naseer Asif]

acd!

thanks for an ideal. I will work on this idea.

[ahsan]

If x belongs to [1,3] and y belongs to [1,4], find the probability that x<y.

Can anyone solve it…

probability is 3/4.
as the probability for interval [1,3] is same for both so probability for [1,4] is increase the 4th part . So probability is 3/4.

[ahsan]

probability is 3/4

[Naseer Asif]

Ahsan, please don't mind i think your answer is probably wrong.

By using acd's idea i have solved the question, which is as follows.

Area of the rectangle above the line y=x

P(x<y) = --------------------------------------------------

Total area of the rectangle

2.5

= ----------

2*3



5/2

= ----------

6



5

= -------
12

A better solution with figure is in attached file. I think it is right answer.

Thanks acd, for the idea.