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It follows that f x (t) = e tx for every tBreak at uniformly chosen point Y • Conditional expectation break again at uniformly chosen point X8GTLXV Hola Gente primero que nada dar las gracias a todos ustedes por Todo su apoyo de verdad Gracias 🙌 No olvides que si te gusto el vídeo me puedes dejar ese like y esa suscripción si

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Y=(x+c)e^-x-I have East the wise equal to y to the natural log of X, and I'm asked to filing derivative using longer It meant differentiation So my firs 💬 👋 We're always here Join our Discord to connect with other students 24/7, any time, night or dayJoin Here!Ie, x and y are either both even or both odd The parity relation is an equivalence relation 1 For any x ∈ ℤ, x has the same parity as itself, so (x,x) ∈ R 2 If (x,y) ∈ R, x and y have the same parity, so (y,x) ∈ R 3 If (x,y) ∈ R, and (y,z) ∈ R, then x and z have the same parity as y, so they have the same parity as each other (if y is odd, both x and z are odd;

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Check out The LambertW function with Fematika, https//youtube/LkJAZXMAKz0 Also try Pythagorean's Triples https//youtube/n6vL2KiWrD4 , Making exponent anThe common log function log(x) has the property that if log(c) = d then 10d = c It's possible to define a logarithmic function log b (x) for any positive base b so that log b (e) = f implies bf = e In practice, we rarely see bases other than 2, 10 and e Solve for y 1 ln(y 1) ln(y − 1) = 2x ln x 2 2log(y 1) = x log(y − 1) 3 2ln y = ln(y 1) x Solve for xx (hint put u Setting x=2 and y=1 in this equation we get c= 5/2 so the particular solution is y^3/3 3y^2/2 x 5/2=0 Thanks!

LECTURE 12 Conditional expectations • Readings Section 43;0 votes 1 answer If x = a e^t(sin t cos t) and y =,a e^t(sin t cos t), then prove that dy/dx = (x y)/(x y) asked in Mathematics by Samantha (3k points) continuity and differntiability;Femminilità e audacia, per donne che vogliono cavalcare con coraggio la quotidianità!

I've been working on this problem for 3 hours now, and my complete lack of progress is getting disheartening I've looked up definitions, proofs, and haveIl commento alle Letture della Domenica e delle Festività A cura di don Claudio DoglioA x B x C C x B x A C x A x B B x B x B Solution A = {a, b, c}, B = {x, y}, and C = {0, 1} are the three given sets A x B x C, C x B x A , C x A x B and B x B x B

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• Given the value y of a rv Y parts of Section 45 EX Y = y= xpno!Linearity of Expectations E P k j=1 c jg j(X) = P k j=1 c jE(g j(X)) 2 If X 1;;X n are independent then E Yn i=1 X i!Solve your math problems using our free math solver with stepbystep solutions Our math solver supports basic math, prealgebra, algebra, trigonometry, calculus and more

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XY (x y) (mean and variance only;If xy = yx, then e x y = e x e y, but this identity can fail for noncommuting x and y Some alternative definitions lead to the same function For instance, e x can be defined as → () Or e x can be defined as f x (1), where f x R → B is the solution to the differential equation df x / dt (t) = x f x (t), with initial condition f x (0) = 1;Scoprite con noi qualche chicca!

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Y = how far up x = how far along m = Slope or Gradient (how steep the line is) b = value of y when x=0 How do you find "m" and "b"? So, y c (x) = C 1 C 2 e x Now for the particular solution I can try Ae x but this is already present in the complementary solution Do I use y p (x) = xAe x Is this the right move at this point in the problem?Click here👆to get an answer to your question ️ cfrom the equation \( y = ( x c ) e ^ { x } \) \( A \) \( E \) \( \frac { d y } { d } y = e ^ { x

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Giovanni PapiniC'è un canto dentro di me (da Opere di Giovanni Papini Volume diciassettesimo Poesia in prosa Cento pagine di Poesia Giorni di Festa Nuo"Rational Solutions to x^y = y^x" CTK Wiki Math "x^y = y^x commuting powers" Arithmetical and Analytical Puzzles Torsten Sillke Archived from the original on dborkovitz () "Parametric Graph of x^y=y^x" GeoGebra OEIS sequence A (Decimal expansion of −x, where x is the negative solution to the equation 2^xHere we have,(frac{d y}{d x}frac{y}{x} c os ec frac{y}{x}=0), y (1) = 0This is an homogenous equation,put y = vx and (frac{d y}{d x}vx frac{d v}{d x})(vx frac{d

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Find c (b) Find P(X Y ≥ 1) (c) Find marginal pdf's of X and of Y (d) Are X and Y independent (justify!) (e) Find E(eX cosY) (f) Find cov(X,Y) We start (as always!) by drawing the support set (See below, left) 2 1 2 1 1 x y=1−x y x y support set Blue subset of support set with y>1−x (a) We find c by setting 1 = Z ∞ −∞ Z ∞ −∞ f(x,y)dydx = Z 1 0 Z 2 0 (cx2E(X) is the expectation value of the continuous random variable X x is the value of the continuous random variable X P(x) is the probability mass function of X Properties of expectation Linearity When a is constant and X,Y are random variables E(aX) = aE(X) E(XY) = E(X) E(Y) Constant When c is constant E(c) = c ProductL y,L z = ih− L x, c L z,L x = ih− L y, d L x,L 2 = 0, e L y,L 2 = 0, f L z,L 2 = 0 8 In exercise 7 above you determined whether or not many of the angular momentum operators commute Now, examine the operators below along with an appropriate given function Determine if the given function is simultaneously an eigenfunction of both operators Is this what you

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E(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 denoted by σ X,Y = Cov(X,Y)Answers and Replies #2 rockfreak667 Homework Helper 6,223 31 Yes, since r=1 is a root of the auxiliary equation, your PI should be Axe x #3E(X)E(Y) in the third equality are utilized, where X and Y are random variables and a is a constant value 139 The variance of X is computed as follows V(X) =V(1 n n i=1 X i) = 1 n2 V(n i=1 X i) = 1 n2 n i=1 V(X i) = 1 n2 n i=1 σ2 = 1 n2 nσ2 = σ2 n We use V(aX) =a2V(X) in the second equality and V(XY) =V(X)V(Y) for X independent of Y in the third equality, where X and Y denote random

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Proof lnexy = xy = lnex lney = ln(ex ·ey) Since lnx is onetoone, then exy = ex ·ey 1 = e0 = ex(−x) = ex ·e−x ⇒ e−x = 1 ex ex−y = ex(−y) = ex ·e−y = ex 1 ey ex ey • For r = m ∈ N, emx = e z }m { x···x = z }m { ex ···ex = (ex)m • For r = 1 n, n ∈ N and n 6= 0, ex = e n n x = e 1 nx n ⇒ e n x = (ex) 1 • For r rational, let r = m n, m, n ∈ NY = −1 4 log(−4(e x C)) = −1 4 log(C −4ex), where we have relabelled the arbitrary constant C (= −4×old value of C) The particular solution is y = −1 4 log(5−4e x) ⁄ Remark The same techniques may also be used to solve PDEs which are separable in the same sense For example, the PDE y ∂u ∂x = u2, only has a derivative with respect to x and so we regard y as fixed and If X = {a, b, c, d, e};

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Solution for y = x – 2 C e* Physics Social ScienceY(0) = 11 A) y = 4 e^2 e^{ x} B) y = e^x 10 e^{ x} C) y = 2 e^x 8 e^{ x} D) Explore over 4,600 video coursesExpected Value and Standard Dev Expected Value of a random variable is the mean of its probability distribution If P(X=x1)=p1, P(X=x2)=p2, n P(X=xn)=pn E(X) =

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Yes No Not Helpful 0 Helpful 0 Ask a Question 0 characters left Include your email address to get a message when this question is answered Submit Advertisement Discussion Differential equations relate a function with one or more of its1 Theory Consider an ordinary differential equation (ode) that we wish to solve to find out how the variable y depends on the variable x If the equation is first order then the highest derivative involved is a first derivative If it is also a linear equation then this means that each term can involve y either as the derivative dy / dx OR through a single factor of yY = mx c is an important reallife equation The gradient, m, represents rate of change (eg, cost per concert ticket) and the yintercept, c, represents a starting value (eg, an admin fee)

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 Explanation dy dx −y −e3x = 0 this is not separable so we use an Integrating Factor (IF) dy dx −y = e3x I F = e∫(−1)dx = e−x ⇒ e−x dy dx −e−xy = e2x Or d dx (e−xy) = e2x e−xy = ∫ e2x dx e−xy = 1 2e2x CH h s wk h x q g lv s x wh g lq j r i wk h r ii u r d g d g y h q wx u h lq y lwh v \ r x wr f olp e lq wr wk h g u ly h u v v h d w d q g h s h u lh q f h h h s oln h q h y h u e h ir u h lwk r y h u f x v wr p l d e oh h h s y h k lf oh v lq f ox g lq j ix wx u lv wlf fStack Exchange network consists of 178 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers Visit Stack Exchange

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= i a2 i Var(X i) 7 The covariance is Cov(X;Y) = E (X x)(Y y) = E(XY) X Y and the correlation is ˆ(X;YHere we will look at solving a special class of Differential Equations called First Order Linear Differential Equations First Order They are "First Order" when there is only dy dx, not d 2 y dx 2 or d 3 y dx 3 etc Linear A first order differential equation is linear when it can be made to look like this dy dx P(x)y = Q(x) Where P(x) and Q(x) are functions of x To solve it there is aJoin for Free Problem $$ x^{2}y^{2}4 x10 y4=0 $$ View

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 The latest tweets from @Y_X_I_X_U_C_EAnswer (1 of 7) e^{(xy)}=x^{y}\\ taking natural log on both sides\\ \ln(e^{(xy)})=\ln(x^{y})\\ (xy)\ln e=y\ln x\\ since, \ln e=1\\ (xy)=y\ln x\\ differentiatingBut then E(XjY =y)=åx xfXjY(xjy)= åx xfX(x)=E(X) 2 2 EE(g(X)jY)=E(g(X)) Proof Set Z = g(X) Statement (i) of Theorem 1 applies to any two rv's Hence, applying it to Z and Y we obtain EE(ZjY)= E(Z) which is the same as EE(g(X)jY)= E(g(X)) 2 This property may seem to be more general statement than (i) in Theorem 1 The proof above shows that in fact these are equivalent

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Answer (1 of 2) Conditional expectation is difficult to work with in the most general case Here is a link to the proof in the general case, but it may not be that informative if you are not familiar with measure theory Law of total expectation I will give you a "proof" in the special caseE(X), then by choosing Y wisely, computing the expected value of E(XjY) can be easier to do than directly computing E(X) Moreover, VarE(XjY) VarX (with equality holding if and only if Xis a deterministic function of Y) Thus not only does E(XjY) have the same expected value as X but is also has a smaller variance This fact can be taken advantage of in stochastic simulation since itAbout Press Copyright Contact us Creators Advertise Developers Terms Privacy Policy & Safety How works Test new features Press Copyright Contact us Creators

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Y = {c, e, f, 4 points= i E(X i) 3 We often write = E(X) 2 4 ˙2 = Var(X) = E((X )2) is the Variance 5 Var(X) = E(X2) 2 6 If X 1;;X n are independent then Var i=1 a iX i!Answer to Solve the initial value problem y' y = 2 e^x;

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Solution for 11 y' y e, y (x c)e, y(0) = %3DSolve your math problems using our free math solver with stepbystep solutions Our math solver supports basic math, prealgebra, algebra, trigonometry, calculus and moreTransforms) x (integral in continuous case) Lecture outline • Stick example stick of length!

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Y = C I G (XM) National income with government interference From the national income, some will be used for consumption, saving, and other's used for paying taxes With adding of variable taxes on national income, then the formula is Y = C S T To see the balance of national income with the adding of government spending and tax variables, can be formulated asB is easy just see where the line crosses the Y axis m (the Slope) needs some calculation m = Change in Y Change in X Knowing this we can work out the equation of a straight line Example 1 m = 2 1 = 2 b = 1 (value of y when x=0) Putting that into y Davneet Singh is a graduate from Indian Institute of Technology, Kanpur He has been teaching from the past 10 years He provides courses for Maths and Science at Teachoo

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 If y^x = e^(y x) prove that dy/dx = (1 log y)^2/log y asked in Mathematics by Samantha (3k points) continuity and differntiability;

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