## anonymous one year ago The probability distribution of X is given in the table. What is the variance of the distribution?

1. anonymous

@rational

2. anonymous

3. rational

start by finding the mean

4. anonymous

um .25?

5. rational

|dw:1432817965592:dw|

6. rational

do you mean `2.5` ?

7. rational

mean = 1*.4+2*.1+3*.1+4*.4 = 2.5

8. anonymous

yes 2.5 sorry.

9. rational

good, find the deviation from mean for each of the data values

10. rational

subtract mean from each data value

11. anonymous

sub. 2.5 to each point?

12. rational

Yes, work \(\large x_i - 2.5\) for each data value

13. rational

|dw:1432818405802:dw|

14. anonymous

-1.5, -.5, .5, 1.5

15. rational

square each of them

16. rational

\(\large (x_i-2.5)^2\)

17. anonymous

-2.25, -.25, .25, 2.25?

18. rational

|dw:1432818549729:dw|

19. rational

when you square, the negative sign disappears thats precicely the reason we square here ok

20. rational

(-1.5)^2 = +2.25 it is not -2.25

21. anonymous

ops, crap. I put it in my calculator wrong then. :/

22. anonymous

@rational so what do I do now?

23. rational

hey still here ?

24. anonymous

yeah.

25. rational

sry was on mobile

26. rational

okay where are we

27. anonymous

Its okay :) 2.25 fix from negative to positive :)

28. rational

|dw:1432819551531:dw|

29. rational

multiply each of those by the corresponding probabilities, then add them up

30. rational

|dw:1432819635519:dw|

31. anonymous

1.85

32. rational

Perfect! 1.85 is the variance

33. rational

we basically used below formula |dw:1432819854547:dw|