Question

Consider a simple example of moral hazard. Suppose that Woodrow goes into a casino to make one bet a day. The casino is very basic; it has two bets: a safe bet and a risky bet. In the safe bet, a nickel is flipped. If the nickel lands on heads, Woodrow wins $ 100 . If it lands on tails, Woodrow loses $ 100 . The risky bet is similar: a silver dollar is flipped. If the silver dollar lands on heads, Woodrow wins $ 5,000 . If it lands on tails, Woodrow loses $ 10,000 . Each coin has a 50 % chance of landing on each side. What is the expected value of the safe bet?

Answer 1

Answer:

The expected value of the safe bet equal $0

Step-by-step explanation:

If  

$S=\left\{s_1,s_2,...,s_n\right\}$

is a finite numeric sample space and

$P(X=s_k)=p_k$ for k=1, 2,..., n

is its probability distribution, then the expected value of the distribution is defined as

$E(X)=s_1P(X=s_1)+s_2P(X=s_2)+...+s_nP(X=s_n)X)$

What is the expected value of the safe bet?

In the safe bet we have only two possible outcomes: head or tail. Woodrow wins $100 with head and “wins” $-100 with tail So the sample space of incomes in one bet is

S = {100,-100}

Since the coin is supposed to be fair,  

P(X=100)=0.5

P(X=-100)=0.5

and the expected value is

E(X) = 100*0.5 - 100*0.5 = 0