To construct a probability distribution table for "X," where "X" refers to the annual profit for this policy, we need to calculate the probability of each outcome and the associated profit.
Let's denote:
M = Major injury
m = Minor injury
N = No injury
1. Probability distribution table for "X":
Outcome (O) Probability (P) Profit (X)
M 1/2000 $15,000 - $200
m 1/500 $4,000 - $200
N 1 - P(M) - P(m) $0 - $200
To calculate the probabilities:
P(M) = 1/2000
P(m) = 1/500
P(N) = 1 - P(M) - P(m)
Now, let's calculate the profits for each outcome:
Profit(M) = $15,000 - $200
Profit(m) = $4,000 - $200
Profit(N) = $0 - $200
2. To compute the expected annual profit that the company can expect to receive per policy holder, we multiply each profit by its corresponding probability and sum them up:
Expected Profit = (Profit(M) * P(M)) + (Profit(m) * P(m)) + (Profit(N) * P(N))
Substituting the values from above:
Expected Profit = ((($15,000 - $200) * 1/2000) + (($4,000 - $200) * 1/500) + (($0 - $200) * (1 - P(M) - P(m)))
Simplifying this expression will give you the expected annual profit that the company can expect to receive per policy holder.