Simple Variance Question

[Big_Jim]

Can somebody calculate the variance for these two situations for me?

I'm a little rusty on my stats, and I think I'm going about it the wrong way

Situation 1:
Getting 1.5:1 on a coin flip

Situation 2:
Getting 6:1 on a single number, on a the roll of a die

Please show all steps.

FWIW: I have the EVs calculated as:

1:
(1.5x-1x)/2 = 0.25x = E(x)

2:
(6x-5x)/6 = 0.167x = E(x)

[BruceZ]

[ QUOTE ]
Can somebody calculate the variance for these two situations for me?

I'm a little rusty on my stats, and I think I'm going about it the wrong way

Situation 1:
Getting 1.5:1 on a coin flip

Situation 2:
Getting 6:1 on a single number, on a the roll of a die

Please show all steps.

FWIW: I have the EVs calculated as:

1:
(1.5x-1x)/2 = 0.25x = E(x)

[/ QUOTE ]

E(x^2) = [(1.5x)^2 + (-1x)^2]/2 = (13/8)*x^2

var(x) = E(x^2) - [E(x)]^2 = (13/8)*x^2 - (0.25x)^2 = (25/16)*x^2


[ QUOTE ]
2:
(6x-5x)/6 = 0.167x = E(x)

[/ QUOTE ]

E(x^2) = (1/6)*(6x)^2 + (5/6)*(-1x)^2 = (41/6)*x^2

var(x) = E(x^2) - [E(x)]^2 = (41/6)*x^2 - (x/6)^2 = (245/36)*x^2

[Big_Jim]

First one:

x1 = +1.5 with p1 = 0.5
x2 = -1 with p2 = 0.5
E(x) = 0.25

v = p1(x1 - E(x))^2 + p2(x2 - E(x))^2

v = 0.5(1.5 - 0.25)^2 + 0.5(-1-0.25)^2

v = 1.5625

Second one:

x1 = 6 with p1 = 0.16666
x2 = -1 with p2 = 0.83333
E(x) = 0.167

v = p1(x1 - E(x))^2 + p2(x2 - E(x))^2

v = 0.1666(6 - 0.167)^2 + 0.83333(-1 - 0.167)^2

v = 6.8055

[Big_Jim]

D'oh, shoulda checked here first.

I just gave a guy $10 in BBV.

Ah well, he deserved it.

[BruceZ]

[ QUOTE ]
D'oh, shoulda checked here first.

I just gave a guy $10 in BBV.

[/ QUOTE ]

You posted this in THREE forums??? In as many hours??? You're a moderator; you should know better. Probability problems go here only, and don't cross post, especially not a routine problem like this one.

[ QUOTE ]
Ah well, he deserved it.

[/ QUOTE ]

FYI, I was the first to give a correct answer 3 minutes after you put a dollar amount on the problem. I also answered in SMP. So I don't deserve to win because I answered in only 2 of the 3 forums you posted, including the correct forum???

[Big_Jim]

[ QUOTE ]
[ QUOTE ]
D'oh, shoulda checked here first.

I just gave a guy $10 in BBV.

[/ QUOTE ]

You posted this in THREE forums??? In as many hours??? You're a moderator; you should know better. Probability problems go here only, and don't cross post, especially not a routine problem like this one.

[ QUOTE ]
Ah well, he deserved it.

[/ QUOTE ]

FYI, I was the first to give a correct answer 3 minutes after you put a dollar amount on the problem. I also answered in SMP. So I don't deserve to win because I answered first in only 2 of the 3 forums you posted, including the correct forum???

[/ QUOTE ]
Whoa whoa, easy now.

I was impatient about the problem, I'll give you that, but I was in the middle of an argument, and wanted my answer fast.

So sue me.

I already shipped the money to him, but it's only $10 bucks, so if you want the prize also, just tell me where to ship it.

Sorry for not looking at the time stamp, earlier, but I already shipped him the money, so I didn't think about it.

[jay_shark]

Hey Jim , just to let you know , you are getting 5:1 against rolling a particular number from a die not 6:1 like you said .

The probability should be 1/6 that you roll a particular number which means odds against of (6-1):1.
I know it's been awhile since you've taken stats but these are some of the mistakes that people make .

[BruceZ]

[ QUOTE ]
Hey Jim , just to let you know , you are getting 5:1 against rolling a particular number from a die not 6:1 like you said .

The probability should be 1/6 that you roll a particular number which means odds against of (6-1):1.
I know it's been awhile since you've taken stats but these are some of the mistakes that people make .

[/ QUOTE ]

He's saying that he's getting PAID 6:1 when his number comes up, not that the odds against rolling his number are 6:1. The odds against rolling his number are 5:1, and that's why he has a positive EV. His EV equations show that he wins 6x when his number comes up, and this has probability 1/6 or odds of 5:1 against, and he loses x when it doesn't come up, and this has probability 5/6.