Consider the transformation Y= 1/X, and the density function f(x) = 3*x² for 01 The density function of Y is non zero for: 1>Y>-1 The density function of Y is non zero for: 0
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- The density function of X is: f(x) = c·x2 ·( 1 - x ). Calculate the mode of X.Let Y possess a density functionf (y) =c(2 − y), 0 ≤ y ≤ 2, 0, elsewher Find c.b Find F(y).c Graph f (y) and F(y).A fish population in a lake satisfies dB/dt=cB(K-B) Fish are then added at A fish per hour. Find the DE for B with respect to t. Is there a new limiting population? If so, what is the solution?
- Suppose X and Y have a joint density function of f(x,y)=6x2y, 0<x<1, 0<y<1. Find P(X+2Y<1).Can I have detailed, step by step explanation for obtaining the answer of the following question? Let Y1 and Y2 have joint density function given by, f(y1, y2) =3(y1) ; 0 <= (y2) <= (y1) <= 1 or 0 ; otherwise Find Cov(Y1, Y2) and correlation coefficient(P).1. Let f (x) = cx 3 and S X = [0, 2] (X is continuous and c is a constant). a. What value of c will make f (x) a valid density?b. What is P (X = 1)?c. What is P (X = 1 or X = 2)?
- laplace transform y" + 2y' + 3y = 100(delta)(t -2) +100(delta)(t - 3) ,y(0)=1, y'(0)=0 Inverse Transforms by Convolution f(t) if L(f) equals: 1/(s-3)(s+5) Inverse Transforms by ConvolutionFind f(t) if L(f) equals: 1/s(s^2 + 4)y''-y'=etcos t , y(0)=0 , y'(0)=0 Laplace TransformTwo college students are studying for an exam. Student X is smarter than sudent Y. The grade that student X receives (x) will take on a value b/w 0 and 1 and the grade that student Y receives (y) will take on a value between 1/3 of x and x. The joint pdf for X and Y are given as: f(x,y) = {6x^2; 0<x<1 , (1/3)x<y<x 0; ew] (i) Find E [Y | X = 0.8] (ii) Find Cov[X,Y]