The expected pay off is $151.16
The variance is $24824.23
The standard deviation is 157.56
<h3>How to solve for the expected pay off</h3>
The red, blue, green and yellow balls are 10 each
the orange ball s 3 each
The total number of balls is
10 + 10 + 10 + 10 + 3
= 43
The number of balls is 1
$0 payoff = green or yellow
$200 payoff = blue
$300 payoff = red
$500 = red
probability of green or yellow = 20 / 43
probability of blue = 10 / 43
probability of red = 10 / 43
probability of orange = 3 / 43
a. What is the expected pay off?
0 * 20 / 43 ) + (200 * 10 / 43) + (300 * 10 / 43) + (500 * 3/43)
= 6500 / 43
= $151.16
B. Variance = e(x²) - e(x)²
0 + 200² * 300² * 500²
(0 * 20 / 43 )+ (40000 * 10 / 43) + (90000 + 10 / 43) + (250000 * 3 / 43)
= 2,050,000 / 43
e(x) = 6500 / 43
2,050,000 / 43 - (6500 / 43)²
$24824.23
standard deviation = √$24824.23
= 157.56
Read more on variance and standard deviation here: brainly.com/question/475676
#SPJ1