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Answer:
The earning to James per year is $ 39,440
The earning of Lin per year is $ 42,540 .
Step-by-step explanation:
Given as :
The total earning of James and Lin together = $ 81,980 per year
The earning of Lin is $ 3100 more per year than James
Let The earning of James = $ J
And The earning of Lin = $ J + $ 3100
So, According to question
The total earning of James and Lin together = $ 81,980 per year
Or, The earning of Lin + The earning of James = $ 81,980 per year
Or, $ J + $ 3100 + $ J = $ 81,980 per year
or, 2 $ J = $ 81,980 - $ 3100
Or, 2 $ J = $ 78880
∴ J =
I.e The earning to James per year = $ 39,440
And The earning of Lin per year = $ 34,440 + $ 3100 = $ 42,540
Hence, The earning to James per year is $ 39,440
And The earning of Lin per year is $ 42,540 . answer
Answer:
The probability mass function for the items sold is
The mean is 96.667
The variance is 22.222
b) The probability mass function for the unfilled demand due to lack of stock is
The mean is 3.333
The variance is 33.333
Step-by-step explanation:
If the demand is higher than 100, then you will sell 100 items only. Thus, there is a probability of 1/3+1/3 = 2/3 that you will sell 100 items, while there is a probability of 1/3 that you will sell 90.
The probability mass function for the items sold is
The mean is 1/3 * 90 + 2/3 * 100 = 290/3 = 96.667
The variance is V(X) = E(X²)-E(X)² = (1/3*90² + 2/3*100²) - (290/3)² = 200/9 = 22.222
b) If order to be unfilled demand, you need to have a demand of 110, which happens with probability 1/3. In that case, the value of the variable, lets call it Y, that counts the amount of unfilled demand due to lack of stock is 110-100 = 10. In any other case, the value of Y is 0, which would happen with probability 1-1/3 = 2/3. Thus
The mean is 2/3 * 0 + 1/3 * 10 = 10/3 = 3.333
The variance is 2/3*0² + 1/3*10² = 100/3 = 33.333