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John is interested in purchasing a multi-office building containing five offices. The current owner provides the following probability distribution indicating the probability that the given number of offices will be leased each year. Number of Lease Offices 0 1 2 3 4 5 Probability 5/18 1/4 1/9 1/18 2/9 1/12 If each yearly lease is $12,000, how much could John expect to collect in yearly leases for the whole building in a given year?(in dollars)
a) E(X) = $23,353.33
b) E(X) = $23,333.33
c) E(X) = $23,273.33
d) E(X) = $23,263.33
e) E(X) = $23,423.33
f) None of the above.

Respuesta :

Answer:

Option B.

Step-by-step explanation:

The given table is:

Number of Lease Offices :  0           1         2       3        4         5

Probability                         : 5/18     1/4     1/9    1/18     2/9      1/12

The expected probability is

Expected probability = [tex]\sum_{i=0}^5 x_{i}p(x_i)[/tex]

Expected probability = [tex]0p(0)+1P(1)+2P(2)+3P(3)+4P(4)+5P(5)[/tex]

Expected probability = [tex]0\cdot (\frac{5}{18})+1\cdot (\frac{1}{4})+2\cdot (\frac{1}{9})+3\cdot (\frac{1}{18})+4\cdot (\frac{2}{9})+5\cdot (\frac{1}{12})=\frac{35}{18}[/tex]

It is given that the yearly lease = $12,000.

The yearly leases for the whole building in a given year is

Yearly leases = [tex]\frac{35}{18}\times 12000=23333.3333333\approx 23333.33[/tex]

Therefore, the correct option is B.

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