 # Copyright 2019 v01 c university of southampton page 4

• 17

Course Hero uses AI to attempt to automatically extract content from documents to surface to you and others so you can study better, e.g., in search results, to enrich docs, and more. This preview shows page 4 - 7 out of 17 pages.

Copyright 2019 v01 cUniversity of SouthamptonPage 4 of 17
5MATH1055W115.[2 marks]LetAbe an×nmatrix that describes a set ofninhomogeneousequations innunknowns:A ~x=~b. This system of equations has a unique solutionif and only if:
16.[2 marks]The solution of the matrix equation1121xy=11is
17.[2 marks]If we writez= 1 +jin the exponential form, one finds that the two rootsofz1/2are
18.[2 marks]A discrete random variable can take the valuesx={0,1,2}withprobabilitiesp=14,12,14. Then, the mean valueμand varianceσ2are given by(a)μ= 1,σ2= 1/2;(b)μ= 0.6,σ2= 1;(c)μ= 0.2,σ2= 1/3;(d)μ= 2,σ2= 2;(e) none of the above.
19.[2 marks]IfXis a normally distributed random variable with mean0and standarddeviation1then the probabilityP(X >1)equals, to4decimal places,
Copyright 2019 v01 cUniversity of SouthamptonTURN OVERPage 5 of 17
6MATH1055W120.[2 marks]Consider a functionf(t, x)of two independent variablestandx. If weintroduce the substitutionsu=x+tandv=x-tthen∂f∂xis equal to(a)-∂f∂u+∂f∂v,(b)-12∂f∂u+12∂f∂v,(c)-12∂f∂u-12∂f∂v,(d)∂f∂u+∂f∂v,(e) none of the above.

Course Hero member to access this document

Course Hero member to access this document

End of preview. Want to read all 17 pages?

Course Hero member to access this document

Term
Summer
Professor
NoProfessor
Tags
c University of Southampton
• • • 