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answer is 18.
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2 answers:
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Answer:
a) The expected value of a die is 3.5
b) The fair value of this game is 4.25 dollars
c) The fair value of this game is 4.6667 dollars
Step-by-step explanation:
a) All the values are equally likely, so to get the expected value of the die we just sum all possible values and divide by the total amount of possible values, 6.
Thus, the expected value of a die is 3.5.
b) The fair value is the expected value of the game. You will reroll the dice only if you expect to get more value on the second throw than what did you obtain on the first one. Since the expected value of a die is 3.5, then you will only reroll the die if you obtain 3 or less, and the probability for that is 1/2.
This means that there is a probability of 1/2 to make a second roll, with expected value 3.5, and a probability of 1/6 to obtain each of 4, 5 or 6 with the first die and keep that value (because it is higher than the expected value from one dice). Therefore, the expected value of this game is
1/2 * 3.5 + 1/6 (4+5+6) = 4.25
The fair value of the game is 4.25 dollars.
c) You can interpret this game as if after your first roll, you can keep that value or play the game described in b, where you roll once and reroll once if you want. Thus, if you decide to decline the value of the first die and reroll, then the expected value of the game will be 4.25. As a result, you will only reroll if you obtain a 4 or lower in the first die, which happens with a probability of 4/6 = 2/3. If you obtain 5 or 6, which happen each case with probability 1/6, you will keep that value because it exceeds your expectations. As a consecuence, the expected value is
2/3 * 4.25 + 1/6*(5+6) = 14/3 = 4.6667
The fair value of the game is 14/3 = 4.6667 dollars.
Answer:
0.18
Step-by-step explanation:
Given that:
P₁ = $10, P₂ = $20
From the tables Q₁ = 900, Q₂ = 800
Using midpoint method:
Percentage change in quantity =
Percentage change in price =
Price of elastic demand = Percentage change in quantity/ Percentage change in price = -11.76% / 66.67% = 0.18
The Price of elastic demand is positive because we took the absolute value and elasticity are always positive
Therefore since Price of elastic demand < 1, the demand is inelastic in this interval.
This means that, along the demand curve between $10 to $20, if the price changes by 1%, the quantity demanded will change by 0.18%. A change in the price will result in a smaller percentage change in the quantity demanded. For example, a 10% increase in the price will result in only a 1.8% decrease in quantity demanded and a 10% decrease in the price will result in only a 1.8% increase in the quantity demanded
