Let C be the curve of intersection of the parabolic cylinder x^2 = 2y, and the surface 3z = xy. Find the exact length of C from the origin to the point (4, 8, 32/3).

Let C be the curve of intersection of the parabolic cylinder x^2 = 2y, and thesurface 3z = xy. Find the exact length of C from the origin to the point (4, 8, 32/3).Let C be the curve of…

 

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Please help with Probability Space functions. The problem is shown in the attachment. I was struggling in understand the concept and I’ll be grateful if you can show me the steps to solutions. Thanks in advance!

6. Let C" be a set in three – dimensional space and let @ ( C ) be equal to the volume of C , if Chas finite*volume ; otherwise , let Q ( O’; be undefined . Find Q ( 0) .( a ) (" = ( ( 2 , 4 , 2) ERS : 0 < < < 2, 0 < 3 < 1 , 0 < < < 3 ).( b ) C = ( ( 2 , 3 , 2) ER 3 : 2 2 + 3 2 + 2 2 2 1 ).7 . For every one – dimensional set C for which the integral exists , Q ( C ) = [of (a ) do , where f ( a ) -Gx ( 1 – 2 ) , 0 < < < 1 , zero elsewhere ; otherwise , let @ ( C") be undefined . Find Q ( C" ) .( a ) (1 = PIER : 1 / 4 < < < 3 / 4)( b ) C 2 = ( 1 / 2}( C ) C3 = PIER : 0 < < < 1018. Suppose the experiment is to choose a real number at randomandom in the interval ( 0 , 1 ) . For any subinterval( a, 6) C ( 0 , 1 ) , it seems reasonable to assign the probability P [ ( a , 6) ] = 6 – a; i.e., the probability ofselecting the point from the subinterval is directly proportional to the length of the subinterval . If thisis the case , choose an appropriate sequence of subintervals to shoe that P [ [a] ] – O for all at ( 0 , 1 )Hint : let ( Chin =I may be a decreasing sequence of events , as in Question 2 , then limn_* too P ( On ) -P ( limn_ too On ) = P (17 = 1 On )`

 

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Let G be a group of order 42.

Prove both (a) and (b).

Prove both (a) and (b).

Prove both (a) and (b).

7 . Let G be a group of order 42 .( a ) Prove that G has a normal subgroup of order 7 .`( b ) Prove that G is a semidirect product of a normal subgroup of order 21 and 2.2 .

 

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Let G be a connected bipartite graph (i.e the set of vertices is split as X S Y so that the edges are connecting some pairs xi ∈ X with yj ∈ Y ). Show that if each vertex has multyplicity 3 then there is a complete matching( i.e the number of vertices in X is the same as in Y and there is matching of all vertices in X with vertices in Y )

 

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This is a statistics question. We need to use RStudio to get the answer of this question. Therefore, this is actually an coding problem in R

Let * follow an exponential distribution with rate parameter &* = 2. Let I" follow a Poisson distributionwith rate parameter^` = $.We write sall I ; for the true standard deviation of I and mall"; for the true median of I".Let s _ he the sample standard deviation of I which is an estimate of sillly. Also let my he the samplemedian which is an Estimate of mill’ ] .Suppose we take samples of size `= = 101 from* and take samples of size my = ]. Consider the statisticWhat is the ( sampling ; distribution of* ! We could ask a statistician who specializes in theary . Instead oflising mathematics . simulate* Good times and stare the results . Plot a histogram of the observed values ofAL . Comment on the shape of the histogram and empirical distribution of* . Before running your code , Set.the same seed used for the previous exercise . For full credit , do not use a For Long.

 

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