The Gaussian distribution in two variables has the form f(x, y) = C'e-²-². See its graph below. What should be so that the total volume below f(x, y) is 1? In other words find C such that: [% f(x,y) dy dx -∞0 C = = 1

Q: If x sin(nx) = f(t) dt, where f is a continuous function, find f(64). %3D f(64) = %3D

A:

Q: 2. Let X have range [0,3] and density f(x) = kx². Let Y = X³. %3D (i) Find k and the cumulative…

A:

Q: Σ If f(x, y) = (xy)", with |xy| < 1, find af and af dx ду n=0

A: Given, fx,y=∑n=0∞xyn, with xy&lt;1 Write the function xyn as a composition of the two functions…

Q: Use the chain rule to show that for any differentiable function f(x), [e/(e) = f(x)e/(=),

A:

Q: Let f(y) be a continuous function. Suppose that f(−10) > 0 and f(10) < 0. Show that there is an…

A:

Q: F(x, y) = (1 − e¯¤x)(1 – е¯³µ), for x ≥ 0, y ≥ 0 and a, ß > 0.

A: The joint cdf of X and Y is

Q: When a certain polyatomic gas undergoes adiabatic expansion, its pressure p and volume V satisfy the…

A: pv1.2=kdifferentiating both side with respect to t∂p∂tv1.2+1.2v0.2∂v∂tp=0∂p∂tv1.2=-1.2v0.2∂v∂tp

Q: SS()dt =x arctan x

A:

Q: Consider the case of a continous variable of interest, call it X. Its density function is given by 1…

A: The values which divide a frequency distribution of a variable into hundred equal parts, are said to…

Q: Suppose X is exponential with parameter λ and Y=e X. Find pdf Y using cdf metho

A: Let X has exponential distribution with parameter λ. The pdf for X is, fx=λe-λx,x&gt;0

Q: The time X (min) for a lab assistant to prepare the equipment for a certain experiment is believed…

A: Solution

Q: Find the mean and variance of the gamma distribution using integration to obtain E(X) and E(X2).…

A: Gamma function is defined as: γα=∫0∞xa-1e-xdx Divide both sides by γα…