a) Let y′′ +xy+y=0 be given.Why does the approachy(x):=e^(λx) does not work? b) Find the potential...

a)

Let

y′′ +xy+y=0

be given.Why does the approachy(x):=e^(λx) does not work?

b) Find the potential P(x, y) attached to the exact ODE

2x sin(y) + x^2 cos(y) y′ = 0

c) Is

(x^2 + y)dx − xdy = 0

exact?

Expert Solution

milcah answered 2 years ago

f(x,y)=3(x+y) 0<x+y<1, 0<x<1, 0<y<1 (a) E(xy|x)=? (b) Cov(x,y)=? (c) x and y is independent? thank you!

Let f(x,y)= (3/2)(x^2+y^2 ) in 0≤x≤1, 0≤y≤1. (a) Find V(X) (b) Find V(Y)

Let X and Y have joint pdf f(x,y)=k(x+y), for 0<=x<=1 and 0<=y<=1. a) Find k. b)...

Let X and Y have joint pdf f(x,y)=k(x+y), for 0<=x<=1 and 0<=y<=1. a) Find k. b) Find the joint cumulative density function of (X,Y) c) Find the marginal pdf of X and Y. d) Find Pr[Y<X2] and Pr[X+Y>0.5]

Find the general solution for the equations: P(x) y"+ xy' - y = 0 a) P(x)=...

Find the general solution for the equations: P(x) y"+ xy' - y = 0 a) P(x)= x b) P(x)= x2 c) P(x) = 1

Consider the boundary value problem X ′′ +λX=0 , X ′ (0)=0 , X′(π)=0 . Find...

Consider the boundary value problem X ′′ +λX=0 , X ′ (0)=0 , X′(π)=0 . Find all real values of λ for which there is a non-trivial solution of the problem and find the corresponding solution.

Let f(x) = a(e-2x – e-6x), for x ≥ 0, and f(x)=0 elsewhere. a) Find a...

Let f(x) = a(e-2x – e-6x), for x ≥ 0, and f(x)=0 elsewhere. a) Find a so that f(x) is a probability density function b)What is P(X<=1)

9. Let S = {[ x y]; in R2 : xy ≥ 0} . Determine whether...

9. Let S = {[ x y]; in R2 : xy ≥ 0} . Determine whether S is a subspace of R2. (A) S is a subspace of R2. (B) S is not a subspace of R2 because it does not contain the zero vector. (C) S is not a subspace of R2 because it is not closed under vector addition. (D) S is not a subspace of R2 because it is not closed under scalar multiplication.

y"+xy=0 center x=0 find two linearly independent solutions centered at x=0

Let X be a exponential random variable with pdf f(x) = λe−λx for x > 0,...

Let X be a exponential random variable with pdf f(x) = λe−λx for x > 0, and cumulative distribution function F(x). (a) Show that F(x) = 1−e −λx for x > 0, and show that this function satisfies the requirements of a cdf (state what these are, and show that they are met). [4 marks] (b) Draw f(x) and F(x) in separate graphs. Define, and identify F(x) in the graph of f(x), and vice versa. [Hint: write the mathematical relationships,...

Let X be a uniform random variable with pdf f(x) = λe−λx for x > 0,...

Let X be a uniform random variable with pdf f(x) = λe−λx for x > 0, and cumulative distribution function F(x). (a) Show that F(x) = 1−e −λx for x > 0, and show that this function satisfies the requirements of a cdf (state what these are, and show that they are met). [4 marks] (b) Draw f(x) and F(x) in separate graphs. Define, and identify F(x) in the graph of f(x), and vice versa. [Hint: write the mathematical relationships,...

Question