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To buy a new house you must borrow $150,000. To do this you take out a $150,000, 30-year, 10 percent mortgage. Your mortgage payments, which are made at the end of each year (one payment each year), include both principal and 10 percent interest on the declining balance. How large will your annual payments be?

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To buy a new house you must borrow $150,000. To do this you take out a $150,000, 30-year, 10 percent mortgage. Your mortgage payments, which are made at the end of each year (one payment each year), include both principal and 10 percent interest on the declining balance. How large will your annual payments be?

G. R. Edwin, Inc., had sales of $6 million during the past year. The cost of goods sold amounted to $3 million. Operating expenses totaled $2.6 million, and interest expense was $30,000. Determine the firm’s tax liability

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G. R. Edwin, Inc., had sales of $6 million during the past year. The cost of goods sold amounted to $3 million. Operating expenses totaled $2.6 million, and interest expense was $30,000. Determine the firm’s tax liability

The following data is from a random sample: 1, 1, 1, 2, 3, 5, 5, 8, 12, 13, 14, 14, 14, 14, 18, 100. Find the first, second and third quartiles.

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The following data is from a random sample:
1, 1, 1, 2, 3, 5, 5, 8, 12, 13, 14, 14, 14, 14, 18, 100.
Find the first, second and third quartiles.

The following data is from a random sample: 5, 1, 3, 3, 8. Compute the sample mean, sample standard deviation and sample median

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The following data is from a random sample: 5, 1, 3, 3, 8.
Compute the sample mean, sample standard deviation and sample median

Suppose X is a random variable with E(X) = 5 and Var(X) = 2. What is E(X2)?

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Suppose X is a random variable with E(X) = 5 and Var(X) = 2. What is E(X2)?

Suppose now that events A, B and C are mutually independent with P(A) = 0.3, P(B) = 0.4, P(C) = 0.5. Compute the following: (Hint: Use a Venn diagram) (i) P(A ∩ B ∩ Cc) (ii) P(A ∩ Bc ∩ C) (iii) P(Ac ∩ B ∩ C)

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Suppose now that events A, B and C are mutually independent with
P(A) = 0.3, P(B) = 0.4, P(C) = 0.5.
Compute the following: (Hint: Use a Venn diagram)
(i) P(A ∩ B ∩ Cc) (ii) P(A ∩ Bc ∩ C) (iii) P(Ac ∩ B ∩ C)

Let C and D be two events with P(C) = 0.25, P(D) = 0.45, and P(C ∩ D) = 0.1. What is P(Cc ∩ D)?

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Let C and D be two events with P(C) = 0.25, P(D) = 0.45, and P(C ∩ D) = 0.1.
What is P(Cc ∩ D)?

20 politicians are having a tea party, 6 Democrats and 14 Republicans. To prepare, they need to choose: 3 people to set the table, 2 people to boil the water, 6 people to make the scones. Each person can only do 1 task. (Note that this doesn’t add up to 20. The rest of the people don’t help.) (a) In how many different ways can they choose which people perform these tasks? (b) Suppose that the Democrats all hate tea. If they only give tea to 10 of the 20 people, what is the probability that they only give tea to Republicans? (c) If they only give tea to 10 of the 20 people, what is the probability that they give tea to 9 Republicans and 1 Democrat?

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20 politicians are having a tea party, 6 Democrats and 14 Republicans. To prepare,
they need to choose:
3 people to set the table, 2 people to boil the water, 6 people to make the scones.
Each person can only do 1 task. (Note that this doesn’t add up to 20. The rest of the
people don’t help.)
(a) In how many different ways can they choose which people perform these tasks?
(b) Suppose that the Democrats all hate tea. If they only give tea to 10 of the 20 people,
what is the probability that they only give tea to Republicans?
(c) If they only give tea to 10 of the 20 people, what is the probability that they give tea
to 9 Republicans and 1 Democrat?

Let X and Y be two continuous random variables with joint pdf 2 f(x, y) = cx y(1 + y) for 0 ≤ x ≤ 3 and 0 ≤ y ≤ 3, and f(x, y) = 0 otherwise. (a) Find the value of c. (b) Find the probability P(1 ≤ X ≤ 2, 0 ≤ Y ≤ 1). (c) Determine the joint cdf of X and Y for a and b between 0 and 3. (d) Find marginal cdf FX(a) for a between 0 and 1. (e) Find the marginal pdf fX(x) directly from f(x, y) and check that it is the derivative of FX(x).

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Let X and Y be two continuous random variables with joint pdf
2 f(x, y) = cx y(1 + y) for 0 ≤ x ≤ 3 and 0 ≤ y ≤ 3,
and f(x, y) = 0 otherwise.
(a) Find the value of c.
(b) Find the probability P(1 ≤ X ≤ 2, 0 ≤ Y ≤ 1).
(c) Determine the joint cdf of X and Y for a and b between 0 and 3.
(d) Find marginal cdf FX(a) for a between 0 and 1.
(e) Find the marginal pdf fX(x) directly from f(x, y) and check that it is the derivative of
FX(x).

Suppose that the cdf of X is given by: F(a) = ⎧ ⎪⎪⎨ ⎪⎪⎩ 0 for a < 0 1 for 0 ≤ a < 2 5 2 for 2 ≤ a < 4 5 1 for a ≥ 4. Determine the pmf of X.

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Suppose that the cdf of X is given by:
F(a) =

⎧
⎪⎪⎨
⎪⎪⎩

0 for a < 0
1 for 0 ≤ a < 2 5
2 for 2 ≤ a < 4 5
1 for a ≥ 4.
Determine the pmf of X.