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Dan works in an insurance company. Last January, he was able to insure 2 persons. Last February, he was able to insure 3 persons. Last March, he was able to insure 5 persons. Assume that samples of size 2 are randomly selected with replacement from this population of three values. a. List down the 9 different possible samples. b. Find the mean of each sample. c. Find the mean of the sampling distribution of means. d. Identify the probability of each sample. e. Find the population mean. f. Compare the population mean with the mean of the sampling distribution of means.
The Mellow Cake corporation is facing a downward sloping demand curve for its Mellow Cakes deserts. In the table below you are provided with information on the firm’s marginal revenues and total costs.
(Note: the Marginal revenues at a level Q in the table are the revenues at level Q+1 minus the revenues at level Q.)
Quantity Produced (Q) Marginal Revenue (Q) Total Cost (Q)
1 40 1
2 35 4
3 30 9
4 25 15
5 20 22
6 15 42
7 10 67
8 5 97
9 0 137
10 -5 187
1. Is the firm in this example a price taking firm? Explain why or why not. (5 pts.)
2. What is the firm’s optimal level of output? Explain why it is optimal. (5 pts.)
In an attempt to deliver the parcel on time, the dispatch rider had to ride 10km 15 degrees SE, he then rode 11km 30 degrees NE and then takes a shortcut at 22km W. How many km did he ride NE and W combined?
One stereoisomer of 1,4 dibromocyclohexane has a melting point of 113 oC, the other isomer melts below 0 oC. Draw both structure and assign melting points to the structures. Justify your choice
Colombo City typically has rained on about 16% of days in November.
a. What is the probability that it will rain on about 16% of days in November?
b. What is the mean number of days with rain in November?
c. What is the variance and standard deviation of the number of days with rain
in November?
Susan and Thomas play a game using two 10p coins. The coins are tossed and
Susan records her score using the random variable S and Thomas records his
score using the random variable T. After a large number of tosses they compare
their scores.
Comment on any likely differences and similarities.
Two fair cubical dice are thrown: one is red and one is blue. The random variable
M represents the score on the red die minus the score on the blue die.
a. Find the distribution of M.
b. Write down E(M).
c. Find Var (M)
Differentiate between ‘discrete’ and ‘continuous’ random variables with
appropriate examples.
Why normal curve is useful in problem solving. Give a real life situation as your own example?
The value of a delivery van depreciates at the rate of 15% per year. Show that
annual depreciation follows a geometric progression, and use this progression
to determine the value of the van after three years, if it is purchased for $4500?
#340153 on Dec 2023