Question

Please find the Standard Deviation of each option

Option A			Option B
Payout	Probability		Payout	Probability
$200	0.05		$100	0.01
$ 50	0.10		$ 55	0.14
$ 25	0.15		$ 35	0.15
$    5	0.20		$ 29	0.20
$    1	0.50		$    1	0.50

Answer 1

MEAN:

Let x be a discrete r.v. with values i=1,2,...,n represent the probability distribution of a r.v. x denote by E(X)  is defined as

VARIANCE:

Let x be a discrete r.v. with if i=1,2,...,n represent the probability distribution of a r.v. x denote by is defined as,

STANDARD DEVIATION:

The positive square root of the variance is called the standard deviation (SD).

OPTION A:

x	pi	pi*x	pi*x*x
200	0.05	10	2000
50	0.1	5	250
25	0.15	3.75	93.75
5	0.2	1	5
1	0.5	0.5	0.5
total	1	20.25	2349.25

E(X^2)=	2349.25
Mean=E(X)=	20.25
(E(X))^2=	410.0625
Variance=V(X)=	1939.188
Standard Deviation=	44.03621

Standard deviation of option A is 44.03621

OPTION B:

x	pi	pi*x	pi*x*x
100	0.01	1	100
55	0.14	7.7	423.5
35	0.15	5.25	183.75
29	0.2	5.8	168.2
1	0.5	0.5	0.5
Total	1	20.25	875.95

E(X^2)=	875.95
Mean=E(X)=	20.25
(E(X))^2=	410.0625
Variance=V(X)=	465.8875
Standard Deviation=	21.58443

Standard deviation of option B is 21.58443