Answer: $6321
Step-by-step explanation:
Expected value is given as exactly what you might think it means intuitively, the return you can expect for some type of action.
The basic expected value formula is the probability of an event multiplied by the amount of times the event happens:(P(x) * n).
he formula for the Expected Value for a binomial random variable is:
P(x) * X.
X is the number of trials and P(x) is the probability of success.
The formula for calculating the Expected Value where there are multiple probabilities is:
E(X) = ∑X * P(X)
The equation is basically the same, but here you are adding the sum of all the gains multiplied by their individual probabilities instead of just one probability.
Calculating the expected value of winning as follows:
Given,
Fx= e^-x, x is greater or equal to 0
Now, P less than or equal to zero =
[-e^-x] ^1
e^-0 - e^-1
= 1 - e^-1
= 0.6321
and P(x>1) = 1-0.6321= 0.3679
Therefore,Let y= amount of winnings.
Based on the above given information,
y= $10000 0
P(y)= 0.6321 0.3679
The expected value of winning:
E(y) = ΣyP(y)
E(y) = 10000 × 0.6321 + 0 × 0.3679
E(y) = $6321
Therefore, the expected value of winning is $6321
