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Estimate P, and find the relative uncertainty in the estimate.

1.  Refer to Exercise 10 in Section 3.2. Assume that τ = 35.2 ± 0.1 Pa, h = 12.0 ± 0.3 mm, and μ = 1.49 Pa · s with negligible uncertainty. Estimate V, and find the relative uncertainty in the estimate.

 

 

2.   Refer to Exercise 5. Assume that P1 = 15.3 ± 0.2 MPa and P2 = 25.8 ± 0.1 MPa. Estimate P3 , and find the relative uncertainty in the estimate.

 

3.  Refer to Exercise 7. Assume that p = 4.3 ± 0.1 cm and q = 2.1 ± 0.2 cm. Estimate f, and find the relative uncertainty in the estimate.

 

4.   Refer to Exercise 8.

 

a.   Assume that P = 224.51 ± 0.04 kPa and V = 11.237 ± 0.002….

Estimate R, and find the relative uncertainty in the estimate.

1.  Refer to Exercise 12. Estimate n, and find the relative uncertainty in the estimate, from the following measurements: θ1 = 0.216 ± 0.003 radians and θ2 = 0.456 ± 0.005 radians.

 

2.   Refer to Exercise 14. Assume that l = 10.0 cm ± 0.5% and d = 10.4 cm ± 0.5%.

 

a.  Estimate R, and find the relative uncertainty in the estimate. Does the relative uncertainty depend on k?

b.   Assume that either l or d can be remeasured with relative uncertainty 0.2%. Which should be remeasured to provide the greater improvement in the relative uncertainty of the resistance?

 

3.   Refer to Exercise 15. Assume that F = 750 ± 1 N, R = 0.65 ± 0.09 mm, L0 = 23.7 ± 0.2 mm,….

Estimate S, and find the relative uncertainty in the estimate.

1.   Refer to Exercise 16. Assume that T0 = 73.1 ± 0.1°F, Ta = 37.5 ± 0.2°F, k = 0.032 min −1 with negligible uncertainty, and T = 50°F exactly. Estimate t, and find the relative uncertainty in the estimate.

 

2.   Refer to Exercise 19. Assume that for a certain bacterium, r = 0.8 ± 0.1 µm and h = 1.9 ± 0.1 µm.

 

a.  Estimate S, and find the relative uncertainty in the estimate.

b.   Estimate V, and find the relative uncertainty in the estimate.

c.    Estimate R, and find the relative uncertainty in the estimate.

d.   Does the relative uncertainty in R depend on c?

 

Find the relative uncertainty in the estimated rate of increase.

1.    Refer to Exercise 5. Assume that the relative uncertainty in P1 is 5% and the relative uncertainty in P2 is 2%. Find the relative uncertainty in P3.

 

2.    Refer to Exercise 14. Assume that the relative uncertainty in l is 3% and that the relative uncertainty in d is 2%. Find the relative uncertainty in R.

 

 

3.   An item is to be constructed by laying three components in a row. The length of each component will be measured.

 

a.  If the uncertainty in measuring the length of each component is 1.2 mm, what is the uncertainty in the combined length of the three components?

b.  If it is desired to estimate the length of the item with an uncertainty of 0.5 mm, what….

Find the relative uncertainty in the estimated proportion.

1.  The Darcy–Weisbach equation states that the power-generating capacity in a hydroelectric system that is lost due to head loss is given by P = ηγQH, where η is the efficiency of the turbine, γ is the specific gravity of water, Q is the flow rate, and H is the head loss. Assume that η = 0.85 ± 0.02, H = 3.71 ± 0.10 m, Q = 60 ± 1m3 /s, and γ = 9800 N/m3 with negligible uncertainty.

 

 

a.  Estimate the power loss (the units will be in watts), and find the uncertainty in the estimate.

b.  Find the relative uncertainty in the estimated power loss.

c.   Which would provide the greatest reduction in the uncertainty in P: reducing the uncertainty in η to 0.01,….

Estimate the resistance of this resistor, and find the uncertainty in the estimate.

1.  Sixteen independent measurements were made of the resistance of a resistor. The average was 52.37 Ω and the standard deviation was 0.12 Ω.

 

a.  Estimate the resistance of this resistor, and find the uncertainty in the estimate. A single measurement is made of the resistance of another resistor.

b.  This measurement is 61.42 Ω. What is the uncertainty in this measurement?

 

2.   The article “Insights into Present-Day Crustal Motion in the Central Mediterranean Area from GPS Surveys” (M. Anzidei, P. Baldi, et al., Geophysical Journal International, 2001:98–100) reports that the components of velocity of the earth's crust in Zimmerwald, Switzerland, are 22.10 ± 0.34 mm/year in a northerly direction and 14.3 ± 0.32 mm/year in an easterly direction.

a.  Estimate the velocity of the earth's….

Which sequence is more likely, HTTHH or HHHHH? Or are they equally likely?

1.  Refer to Exercise 23. Assume that the probabilities that each of the three scenarios occurs are P(A) = 0.20, P(B) = 0.30, and P(C) = 0.50.

a.   Find the probability that scenario A occurs and that the loss is 5%.

b.  Find the probability that the loss is 5%.

c.    Find the probability that scenario A occurs given that the loss is 5%.

 

2.  A box contains four 75 W lightbulbs, three 60 W lightbulbs, and three burned-out lightbulbs. Two bulbs are selected at random from the box. Let X represent the number of 75 W bulbs selected, and let Y represent the number of 60 W bulbs selected.

a.  Find the joint probability mass function of X and Y.

b.  Find µX .

c.    Find….

Find the marginal probability mass functions pX (x) and pY (y).

1.  A penny and a nickel are tossed. The penny has probability 0.4 of coming up heads, and the nickel has probability 0.6 of coming up heads. Let X = 1 if the penny comes up heads, and let X = 0 if the penny comes up tails. Let Y = 1 if the nickel comes up heads, and let Y = 0 if the nickel comes up tails.

a.  Find the probability mass function of X.

b.  Find the probability mass function of Y.

c.   Is it reasonable to assume that X and Y are independent? Why?

d.   Find the joint probability mass function of X and Y.

2.  Two fair dice are rolled. Let X represent the number on the first die, and let Y represent….

Find the joint probability mass function of X and Y.

1.  Refer to Exercise 31. Assume the first card is not replaced before the second card is drawn.

a.  Find the joint probability mass function of X and Y.

b.  Find the marginal probability mass functions pX (x) and pY (y).

c.    Find µX and µY .

d.   Find µXY.

e.   Find Cov(X,Y)

 

2.    Blood is taken from each of n individuals to be tested for a certain disease. Rather than test each sample separately, a pooled method is used in an attempt to reduce the number of tests needed. Part of each blood sample is taken, and these parts are combined to form a pooled sample. The pooled sample is then tested. If the result is negative, then none of the n individuals has the disease,….

Is it possible to tell which thermometer is more precise?

1.  The boiling point of water is measured four times. The results are 110.01°C, 110.02°C, 109.99°C, and 110.01°C. Which of the following statements best describes this measuring process?

b.  Accurate but not precise

c.    Precise but not accurate

d.   Neither accurate nor precise

e.  Both accurate and precise

 

2.   Two thermometers are calibrated by measuring the freezing point of glacial acetic acid, which is 16.6°C. Equal numbers of measurements are taken with each thermometer. The result from the first thermometer is 16.4 ± 0.2°C and the result from the second thermometer is 16.8 ± 0.1°C.

 

a.   Is it possible to tell which thermometer is more accurate? If so, say which one. If not, explain why.

b.  Is it possible to tell which thermometer is more precise?….