1. For the function z x + y, show that its uncertainty is oz-(o2+o)122. For the function z = xy, show that its uncertainty is o, z*((o/x )2 + (oyly))1/2. HINT: start with o,/z and simply the algebra3. For the following functions, a) solve for o, and b) redefine your solution in terms of z. (HINT: start with o,/2 and simply the algebra)z Ayx, where we assume A is a constant1/2where we assume A is a constantZEA(x/y)4. In this problem, w f (x, y, z), where we know the values of the measured quantities x, y and z. The results are given as x (5.1+0.1)m, y (9015)cm and z (4.1+0.1)m(a) Now let's say that the function w x-y-z. Solve for w = w+ w based on the results(b) From (a), how many sigmas does the theoretical value w 0 fall into? Based on this number, do the measurements agree with the accepted value of w (explain briefly)?

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Asked Nov 13, 2019
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1. For the function z x + y, show that its uncertainty is oz-(o2+o)12
2. For the function z = xy, show that its uncertainty is o, z*((o/x )2 + (oyly))1/2. HINT: start with o,/z and simply the algebra
3. For the following functions, a) solve for o, and b) redefine your solution in terms of z. (HINT: start with o,/2 and simply the algebra)
z Ayx, where we assume A is a constant
1/2
where we assume A is a constant
ZEA(x/y)
4. In this problem, w f (x, y, z), where we know the values of the measured quantities x, y and z. The results are given as x (5.1+0.1)m, y (9015)cm and z (4.1+0.1)m
(a) Now let's say that the function w x-y-z. Solve for w = w+ w based on the results
(b) From (a), how many sigmas does the theoretical value w 0 fall into? Based on this number, do the measurements agree with the accepted value of w (explain briefly)?
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1. For the function z x + y, show that its uncertainty is oz-(o2+o)12 2. For the function z = xy, show that its uncertainty is o, z*((o/x )2 + (oyly))1/2. HINT: start with o,/z and simply the algebra 3. For the following functions, a) solve for o, and b) redefine your solution in terms of z. (HINT: start with o,/2 and simply the algebra) z Ayx, where we assume A is a constant 1/2 where we assume A is a constant ZEA(x/y) 4. In this problem, w f (x, y, z), where we know the values of the measured quantities x, y and z. The results are given as x (5.1+0.1)m, y (9015)cm and z (4.1+0.1)m (a) Now let's say that the function w x-y-z. Solve for w = w+ w based on the results (b) From (a), how many sigmas does the theoretical value w 0 fall into? Based on this number, do the measurements agree with the accepted value of w (explain briefly)?

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Expert Answer

Step 1

As you have posted 4 different questions, we are answering the first question. In case you require the unanswered questions also, kindly re-post them as separate questions.

Step 2

1.

 

From the given information, the function is z=x+y.

 

Let us assume that the variables x and y are independent. Hence, Covariance(x, y)=0.

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Var (x) o Var(y) Var()= o Cov (x, y) 0

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Step 3

Consider...

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Var ()Var(x+y) =Var (x)+Var (y)+2Cov (x, y)

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