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A phenomena that happens to a computer's keyboard when a human being is bored to deathMany of these are synthesized as inactive precursor zymogens that are cleaved during limited proteolysis to generate their active forms Alignment contains also inactive enzymes that have substitutions of the catalytic triad residuesSTAT 400 Joint Probability Distributions Fall 17 1 Let X and Y have the joint pdf f X, Y (x, y) = C x 2 y 3, 0 < x < 1, 0 < y < x, zero elsewhere a) What must the value of C be so that f X, Y (x, y) is a valid joint pdf?b) Find P (X Y < 1)c) Let 0 < a < 1 Find P (Y < a X) d) Let a > 1 Find P (Y < a X)e) Let 0 < a < 1 Find P (X Y < a)
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G(x,y)f(x,y)dxdy continuous case If g(X,Y)=aX bY, then we can obtain EaX bY=aEXbEY Example 3 At a party N men throw their hats into the center of a room The hats are mixed up and each man randomly selects one Find the expected number of men who select their own hatsExample 6 X and Y are independent, each with an exponential(λ) distribution Find the density of Z = X Y and of W = Y −X2 Since X and Y are independent, we know that f(x,y) = fX(x)fY (y), giving us f(x,y) = ˆ λe−λxλe−λy if x,y ≥ 0 0 otherwise The first thing we do is draw a picture of the support set the first quadrant (a)0 nul 1 soh 2 stx 3 etx 4 eot 5 enq 6 ack 7 bel 8 bs 9 ht 10 nl 11 vt 12 np 13 cr 14 so 15 si 16 dle 17 dc1 18 dc2 19 dc3 dc4 21 nak 22 syn 23 etb 24 can
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411 Recognize a function of two variables and identify its domain and range 412 Sketch a graph of a function of two variables 413 Sketch several traces or level curves of a function of two variables 414 Recognize a function of three or more variables and identify its level surfaces Our first step is to explain what a function ofSimple and best practice solution for (xy)=50 equation Check how easy it is, and learn it for the future Our solution is simple, and easy to understand,X yA y x Resultant force Over a body of constant thickness in x and y W n i F z W i 1 W dW Location x, y is the equivalent location of the force W from all W i's over all x & y locations (with respect to the moment from each force) from M x W xW n i y i i 1 W W xdW x xdW x OR W x W x M y W y W n i x i i 1 W
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R2 given by F(x,y)=(xy,x1) is not linear Solution (a) The operator T is surjective if for any u 2 R 2 there exists v 2 R 2 such that T(v)=uThis requires me to solve the equation (yW 18 x 5 46 ° −1 8 C D 4 12) C A Q 10 x − 10 12 x − 4 30 ° B 12 13) A D B 15 x 5 1 ° 22 x 4 C 3 14) D B V 9x − 2 x 5 40 ° C 3 Find the measure of the angle indicated 15) Find m∠S J R 3x 4 140 ° 8x 4 S T 40 ° 16) Find m∠H F D 14 x 1 ° 5x − 7 G H 38 ° 17) Find m∠FAB C A F 13 x − 3 3x 2 55 If you were installing a NEMA 1530 device, which does not have a neutral, the terminals would be marked X Y Z and G In each case, the X Y or Z terminals designate "hot" lines The use of W indicates a white or neutral connection, and G always is for the grounding connection
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In fact, provided the condition above holds (ie, there exists a feasible x with ¯cTx ≥ α) we can solve the problem (1) via convex optimization We make the change of variables y = x ¯cTx−α, s = 1 ¯cTx−α, so x = y/s This yields the problem minimize q yTRy subject toXfX,Y (x,y)dxdy Now suppose we have a function g(x,y) from R2 to R Then we can define a new random variable by Z = g(X,Y) In a later section we will see how to compute the density of Z from the joint density of X and Y We could then compute the mean of Z using the density of Z Just as in the discrete case there is a shortcut Theorem 1X c (y) = channel depth (varies along the length of the channel) n(x,y)= electron concentration at point (x,y) n (x,y)=the mobility of the carriers at point (x,y) Device width is Z Channel Length is L Assume a "Long Channel" device (for now do not worry about the channel length modulation effect)
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Graph y=x Use the slopeintercept form to find the slope and yintercept Tap for more steps The slopeintercept form is , where is the slope and is the yintercept Find the values of and using the form The slope of the line is the value of , and the yintercept is the value of SlopeE(X Y) = E(X)E(Y) (4) If X and Y are independent, then Var(X Y) = Var(X)Var(Y) (5) The above properties generalize in the obvious fashion to to any finite number of rvs In general (independent or not) Var(X Y) = Var(X)V(Y)2Cov(X,Y), where Cov(X,Y) def= E(XY)−E(X)E(Y), is called the covariance between X and Y, and is usually(b) Construct a DAG for the following program code x=y*z w=py y=y*z p=wx 3 (a) Explain the different issues in the design of a code generator (b) Generate code for the following C statements i x= f(a) f(a) f(a) ii x= f(a) /g(b,c) iii x= f(f(a)) iv x= f(a) 4(a) Write about global register allocation strategy for loops
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•Say there is a new constraint, h(x,y,z)=c So there are numbers λ and μ (called Lagrange multipliers) such that ∇ f(x 0,y 0,z 0) =λ ∇ g(x 0,y 0,z 0) μ ∇ h(x 0,y 0,z 0) The extreme values are obtained by solving for the five unknowns x, y, z, λ and μ This is done by writing the aboveUis the union of the 1st and 3rd quadrant of R2, ie the set f(x;y) xy 0g (In general, any cone (In general, any cone will have the property of being closed under scalar multiplication, where a cone is a set bounded byEC02 Spring 06 HW5 Solutions 6 Problem 343 • X is an Erlang (n,λ) random variable with parameter λ = 1/3 and expected value EX =
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