## schmidtdancer 2 years ago Consider a uniform distribution created by a random number generator. The distribution looks like a square with a length of 1 and a height of 1. The random number generator creates any number between 0 and 1. Find the following probabilities: a) P(0 <= X <= 0.4) b) P(0.4 <= X <= 1) c) P(X > 0.6) d) P(X <= 0.6) e) P(0.23 <= X <= 0.76)

1. schmidtdancer

@ParthKohli @hba ??

2. schmidtdancer

(a) I know a is 0.4

3. mathmate

|dw:1358086275602:dw| Here's how you get it.

4. schmidtdancer

ok so a would then be 0.4?

5. mathmate

Yes, as you said. Remember the area under a probability distribution always add up to 1.0.

6. schmidtdancer

Ok! how do i find b?

7. mathmate

Probability(a<X<b)=area between the vertical lines a and b.

8. schmidtdancer

is it .6?

9. mathmate

Exactly!

10. schmidtdancer

c?

11. mathmate

12. schmidtdancer

um....4?

13. schmidtdancer

.4?

14. mathmate

Yep! Good again!

15. schmidtdancer

Ok! would d be .4 too then

16. schmidtdancer

P(X <= 0.6)

17. mathmate

Can you repeat for d? Draw the diagram and check.

18. schmidtdancer

x is less then or eqaual to .6.....

19. mathmate

The area is....

20. schmidtdancer

hmm

21. schmidtdancer

im not sure how to find this probability?

22. mathmate

The figure is similar to the one I drew, but the vertical line is at 0.6.

23. schmidtdancer

.7?

24. mathmate

X varies from 0 to 1, so X<0.6 means from 0 to 0.6

25. mathmate

|dw:1358086899713:dw|

26. schmidtdancer

.6?

27. schmidtdancer

thats 60 % of the diagram

28. mathmate

Right again!

29. schmidtdancer

ok so d is .6? :)

30. schmidtdancer

and e is .53?

31. mathmate

You do realize that we are dealing with a square of 1x1. So 0<X< 0.6 means simply 60% of the square. Sometimes, and most of the time, the distribution is not a straight line (uniform), the calculation may not be as easy. Such as this: |dw:1358087084888:dw| You're doing great with this particular case. ALSO NOTICE that we did not care between <= (less than or equal) and < less than. It is because P(x=0.6) is zero, because it is almost impossible for X to be exactly 0.6. Finally, for (e), you got it right again, congratulations!