Que 1
Expected payoff is the sum of probability adjusted payoff across all the possible outcomes = Xe =
where Pi is the probability of payoff Xi
= 1 x 11/36 + 2 x 9/36 + 3 x 7/36 + 4 x 5/36 + 5 x 3/36 + 6 x 1 / 36 = $ 91 / 36 mn = $ 2.53 mn
Que 2
Variance of discrete distribution, 2
where Xe = expected payoff as calculated in Que 1 above
= (1 - 2.53)2 x 11/36 + (2 - 2.53)2 x 9/36 + (3 - 2.53)2 x 7/36 + (4 - 2.53)2 x 5/36 + (5 - 2.53)2 x 3/36 + (6 - 2.53)2 x 1 / 36 = 1.971451
Standard deviation, = = $ 1.40 mn
Que 3
Expected gain / loss = Expected payoff - cost of the lottery ticket = $ 2,527,778 - 100 = $ 2,527,678
Que 4
Future compounded expected payoff = Future Value of expected payoff Xe = Xe x (1 + R)N where R = interest rate = 5% per annum and N = period = 5 years
Hence, Future compounded expected payoff = 2.53 x (1 + 5%)5 = $ 3.23 mn
Que 5
Yes, there is a correlation between the payoff amount X and the probability associated with it. The probability of the payoff declines as payoff amount increase.
Que 6
As X increases, probability decreases. So, if probability is dependent variable and payoff, X is independent variable then, the depended variable decreases in value as the value of independent variable increase. So, the sign of the regression coefficient must be negative.
Que 7
Regression coefficient is the coefficient of independent variable in the equation of regression. If Y = aX + b is the linear regression equation connecting X and Y, then Y is the dependent variable and X is the independent variable. Regression coefficient will then be "a", the coefficient of X in the equation of regression. Thus regression coefficient measures the change in the value of dependent variable for a unit change in the value of independent variable. Thus it is also an indicator of sensitivity of dependent variable with respect to independent variable.
Que 8
P value test tells us whether the regression coefficients are significant or not.
The P value in turn is dependent upon t statistics and degrees of freedom.
If P value is less than the common alpha level of 0.05, then the coefficient is statistically significant otherwise it's not.
1. Multi-millionaire lottery Suppose you bought a lottery ticket at $100 today, January 5, 2018. You...
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