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The treasurer of Company ABC expects to receive a cash inflow of $18,000,000 in 90 days. The treasurer expects short-term interest rates to fall during the next 90 days. To hedge against this risk, the treasurer decides to use an FRA that expires in 90 days and is based on 90-day LIBOR. The FRA is quoted at 6%. At expiration, LIBOR is 4.8%. Assume that the notional principal on the contract is $18,000,000. i. Indicate whether the treasurer should take a long or short position to hedge interest rate risk. ii. Using the appropriate terminology, identify the type of FRA used here. iii. Calculate the gain or loss to Company ABC as a consequence of entering the FRA
Determine whether T is linear transformation or not.
T:R2−→R3
T (x,y )= (x-y,x+y,2x)
What is the truth values for the Compound Proposition:
(P =>Q) => R
Describe the Hasse Diagram for the divisibility of the set A = {1, 2, 3, 5, 6 10, 15, 30}For which situation Poisson distribution is appropriate to calculate probability of a random event.
The manager of a fleet automobiles is testing two brands of radial tires and assigns
one tire of each brand at random to the two rear wheels of eight cars and runs the
cars until the tires wear out. The data (in kilometers) follow.
Car Brand 1 Brand 2
1 36,925 34,318
2 45,300 42,280
3 36,240 35,500
4 32,100 31,950
5 37,210 38,015
6 48,360 47,800
7 38,200 37,810
8 33,500 33,215
Do the data suggest that the two brands of radial tires prove the same mean life? Use
α = 0.01. [taken from Montgomery, p. 354]
The diameter of steel rods manufactured on two different extrusion machines are
being investigated. Two random samples of sizes "n_1" = 15 and "n_2" = 17 are selected,
and the sample means and sample variances are x̅1 = 8.73, "s_1^2" = 0.35, x̅2 =8.68, and "s_2^2" = 0.40, respectively. Assume that "\\sigma_1^2=\\sigma_2^2"
and that data are drawn from
a normal distribution. (a) Is there evidence to support the claim that the two
machines produce rods with different mean diameters? Use α = 0.05 in arriving at
this conclusion. (b) Find the P-value for the t-statistic you calculated in part (a).
[taken from Montgomery, p. 347]
Two companies manufacture a rubber material intended for use in an automotive
application. The part will be subjected to abrasive wear in the field application, so we
decide to compare the material produced by each company in a test. Twenty-five samples of material from each company are tested in an abrasion test, and the amount
of wear after 1000 cycles is observed. For company 1, the sample mean and standard
deviation of wear are x̅1 = 20 milligrams/1000 cycles and s1 = 2 milligrams/1000
cycles, while for company 2 we obtain x̅2 = 15 milligrams/1000 cycles and s2 = 8
milligrams/1000 cycles. [taken from Montgomery, p. 348]
(a) Do the data support the claim that the two companies produce material with
different mean wear? Use α = 0.05, and assume each population is normally
distributed but that their variances are not equal.
(b)What is the P-value for this test?
(c) Do the data support a claim that the material from company 1 has a higher mean
wear than the material from company 2?
Cloud seeding has been studied for many decades as a weather modification
procedure. The rainfall in acre-feet from 20 clouds follows:
18.0 30.7 19.8 27.1 22.3 18.8 31.8 23.4 21.2 27.9
31.9 27.1 25.0 24.7 26.9 21.8 29.2 34.8 26.7 31.6
Can you support the claim that mean rainfall from seeded clouds exceeds 25 acre-
feet? Use α = 0.01. Assume that rainfall is normally distributed. [taken from
Montgomery, p. 306]
An engineer who is studying the tensile strength of a steel alloy intended for use in
golf club shafts knows that tensile strength is approximately normally distributed
with σ = 60 psi. A random sample of 12 specimens has a mean tensile strength of x̅=
3250 psi. (a) Test the hypothesis that mean strength is 3500 psi. use α = 0.01. (b)
What is the smallest level of significance at which you would be willing to reject the
null hypothesis? [taken from Montgomery, p. 300]
