1) A set of 13 measurements are obtained with the values 0, 1, 2, 3, 4,...
1) A set of 13 measurements are obtained with the values 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10,11, 12, each of which is found once. Find the average value of the measurements and thestatistical uncertainty based on the measurements. Consider the function n= 1/Lfor 0≤x≤Land n= 0 otherwise. Find theaverage value of x and its spread. Compare the two results. (Use appropriate integrals instead of the sums you used in the previous problem.)
Homework Answers
1) the average value is = 
Statistical uncertainty=sample standard deviation=
where n=13
Then 
s=3.89
2)
Add Answer to:
1) A set of 13 measurements are obtained with the values 0, 1,
2, 3, 4,...
figure 2.3 EXPERIMENT Experimental Uncertainty (Error) and Data Analysis 2 Laboratory Report TI QUESTIONS 1. Read...
figure 2.3
EXPERIMENT Experimental Uncertainty (Error) and Data Analysis 2 Laboratory Report TI QUESTIONS 1. Read the measurements on the rulers in Fig. 2.9, and comment on the results Ruler 1 om 5 Ruler 2 cm 6 Ruler 3 TTm 6 Figure 2.9 2. Were the measurements of the block in part tb) of Procedure 2 all done with the same instrument? Explain. 3. Referring to the dart analogy in Fig. 2.3, draw a dart grouping that would represent poor...
(1) Suppose the pdf of a random variable X is 0, otherwise. (a) Find P(2 <...
(1) Suppose the pdf of a random variable X is 0, otherwise. (a) Find P(2 < X < 3). (b) Find P(X < 1). (e) Find t such that P(X <t) = (d) After the value of X has been observed, let y be the integer closest to X. Find the PMF of the random variable y U (2) Suppose for constants n E R and c > 0, we have the function cr" ifa > 1 0, otherwise (a)...
Only do exerice 1-9 220AL-E1 he uncertainty in an experimental quantity must be reported. Since there...
Only do exerice 1-9
220AL-E1 he uncertainty in an experimental quantity must be reported. Since there are a number of ways to do this we must state the meaning of the uncertainty. A Estimated uncertaint Sometimes we make several measurements that are identical. Eq 1-2 would yield ơx-0, which could lead to the mistaken impression that the uncertainty is zero when in fact the precision of the instrument is less than the random errors. We must estimate the uncertainty, and,...
#1 #2 A set of real numbers is graphed. 4 > -6 -1 0 1 2...
#1
#2
A set of real numbers is graphed. 4 > -6 -1 0 1 2 3 WebAssign. Numberline Find an inequality involving an absolute value that describes the set. (Let x represent a real number in the set.) A set of real numbers is graphed. Ho -4 -3 -1 0 1 3 5 O WebAssign. NumberLine Find an inequality involving an absolute value that describes the set. (Let x represent a real number in the set.)
Given the following two sequences x (n)=[3 , 11,7 ,0 ,−1, 4 ,2 ],−3≤n≤ 3 ;...
Given the following two sequences x (n)=[3 , 11,7 ,0 ,−1, 4 ,2 ],−3≤n≤ 3 ; h (n )=[2,3 ,0 ,−5, 2,1 ] ,−1≤n≤ 4. (a) Use the deiniion to determine the convoluion y ( n )= x ( n )∗h (n ) (b) Compare your result in (a) with that obtained by MATLAB
13 please 8. b. -2 3 0 0 0 0 -1 2 0 0-4 0 3...
13 please
8. b. -2 3 0 0 0 0 -1 2 0 0-4 0 3 0-2 0 3 0 0 -2 0 3 0 4 o0-1 6 0 0 1 o 2 6 0 0 -1 6 10. For any positive integer k, prove that det(4t) - de(A)*. 11. Prove that if A is invertible, then den(A-1)- I/der(A) - det(4)- 12. We know in general that A-B丰B-A for two n x n matrices. However, prove that: det(A . B)-det(B...
2. Consider the following pseudocode for a disjoint-set implementation: Make-Set Cx) rank ) 0 Find-Set(x) return...
2. Consider the following pseudocode for a disjoint-set implementation: Make-Set Cx) rank ) 0 Find-Set(x) return Find-Set (pLx) return LinkCx, y if rank]rank[y] else if rankx)rank y) rank[y]ran[y]1 Union (,y) Link (Find-Set (x), Find-Set(y)) Show the data structure that results and the answers returned by the Find-Set operations in the following program for i ? 1 to 16 Make-Set() for i ? 1 to 15 by 2 Union, ) for i1 to 13 by 4 UnionC, 2) UnionCi xs) Union(x11,...
2. The boundary value problem y" + ly = 0, y'(0)= 0 , y'(1) = 0)...
2. The boundary value problem y" + ly = 0, y'(0)= 0 , y'(1) = 0) has normalized eigenfunctions 6(x)=1, 0,,(x) = V2 cos nix, n=1,2,3,... a. Using the method of eigenfunction expansion, solve the boundary value problem y " + 8y = x , y'(0)= 0, y'(1)=0 Set up, but do not evaluate, the required integrals. b. Determine how many solutions the below boundary value problem has. y" + 257² y = sinº 5ax , y(0) = 0 ,...
only one problem (Exercise 1-11 only) Uncertainties in Measurement and Propagation of Errors one measurement is...
only one problem (Exercise 1-11 only)
Uncertainties in Measurement and Propagation of Errors one measurement is made and often the peecision of the instrument is used as arn mate of the uncertainty. the instrument and the situation, the uncertainty Depending upon could be less than the precision of the instrument or it could be more. For example, in measuring we may estimate the distance between the small est subdivision (mm) if we rurn the meter stick onto its side to...
ONLY NUMBER 2 1. Find the CTFS coefficients of the periodic signal 1 1-4 」E [0, 1] 0 otherwise 2. In this problem you will practice using properties to derive the CTFS coefficients of 0 otherwise...
ONLY NUMBER 2
1. Find the CTFS coefficients of the periodic signal 1 1-4 」E [0, 1] 0 otherwise 2. In this problem you will practice using properties to derive the CTFS coefficients of 0 otherwise from the CTFS coefficients of a(t) from the previous problem. (a) What is the periodic convolution of r(t) with itself? (b) How is the periodic convolution of r(t) with itself related to y(t) (c) Find the coefficients of y(t) by applying CTFS properties, selected...
figure 2.3
EXPERIMENT Experimental Uncertainty (Error) and Data Analysis 2 Laboratory Report TI QUESTIONS 1. Read the measurements on the rulers in Fig. 2.9, and comment on the results Ruler 1 om 5 Ruler 2 cm 6 Ruler 3 TTm 6 Figure 2.9 2. Were the measurements of the block in part tb) of Procedure 2 all done with the same instrument? Explain. 3. Referring to the dart analogy in Fig. 2.3, draw a dart grouping that would represent poor...
(1) Suppose the pdf of a random variable X is 0, otherwise. (a) Find P(2 < X < 3). (b) Find P(X < 1). (e) Find t such that P(X <t) = (d) After the value of X has been observed, let y be the integer closest to X. Find the PMF of the random variable y U (2) Suppose for constants n E R and c > 0, we have the function cr" ifa > 1 0, otherwise (a)...
Only do exerice 1-9
220AL-E1 he uncertainty in an experimental quantity must be reported. Since there are a number of ways to do this we must state the meaning of the uncertainty. A Estimated uncertaint Sometimes we make several measurements that are identical. Eq 1-2 would yield ơx-0, which could lead to the mistaken impression that the uncertainty is zero when in fact the precision of the instrument is less than the random errors. We must estimate the uncertainty, and,...
#1
#2
A set of real numbers is graphed. 4 > -6 -1 0 1 2 3 WebAssign. Numberline Find an inequality involving an absolute value that describes the set. (Let x represent a real number in the set.) A set of real numbers is graphed. Ho -4 -3 -1 0 1 3 5 O WebAssign. NumberLine Find an inequality involving an absolute value that describes the set. (Let x represent a real number in the set.)
13 please
8. b. -2 3 0 0 0 0 -1 2 0 0-4 0 3 0-2 0 3 0 0 -2 0 3 0 4 o0-1 6 0 0 1 o 2 6 0 0 -1 6 10. For any positive integer k, prove that det(4t) - de(A)*. 11. Prove that if A is invertible, then den(A-1)- I/der(A) - det(4)- 12. We know in general that A-B丰B-A for two n x n matrices. However, prove that: det(A . B)-det(B...
2. Consider the following pseudocode for a disjoint-set implementation: Make-Set Cx) rank ) 0 Find-Set(x) return Find-Set (pLx) return LinkCx, y if rank]rank[y] else if rankx)rank y) rank[y]ran[y]1 Union (,y) Link (Find-Set (x), Find-Set(y)) Show the data structure that results and the answers returned by the Find-Set operations in the following program for i ? 1 to 16 Make-Set() for i ? 1 to 15 by 2 Union, ) for i1 to 13 by 4 UnionC, 2) UnionCi xs) Union(x11,...
2. The boundary value problem y" + ly = 0, y'(0)= 0 , y'(1) = 0) has normalized eigenfunctions 6(x)=1, 0,,(x) = V2 cos nix, n=1,2,3,... a. Using the method of eigenfunction expansion, solve the boundary value problem y " + 8y = x , y'(0)= 0, y'(1)=0 Set up, but do not evaluate, the required integrals. b. Determine how many solutions the below boundary value problem has. y" + 257² y = sinº 5ax , y(0) = 0 ,...
only one problem (Exercise 1-11 only)
Uncertainties in Measurement and Propagation of Errors one measurement is made and often the peecision of the instrument is used as arn mate of the uncertainty. the instrument and the situation, the uncertainty Depending upon could be less than the precision of the instrument or it could be more. For example, in measuring we may estimate the distance between the small est subdivision (mm) if we rurn the meter stick onto its side to...
ONLY NUMBER 2
1. Find the CTFS coefficients of the periodic signal 1 1-4 」E [0, 1] 0 otherwise 2. In this problem you will practice using properties to derive the CTFS coefficients of 0 otherwise from the CTFS coefficients of a(t) from the previous problem. (a) What is the periodic convolution of r(t) with itself? (b) How is the periodic convolution of r(t) with itself related to y(t) (c) Find the coefficients of y(t) by applying CTFS properties, selected...
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