X~exp(λ) with λ=1
1) define Y= X^1/2. Find the support of Y and its density.
2) define Z = X^2 + 2X. Find the support of Z and its density.
X~exp(λ) with λ=1 1) define Y= X^1/2. Find the support of Y and its density. 2)...
Let X be exponential random variable with λ = 1. (a) Define Y = √ X. Specify the support of Y and find its density. (b)Define Z = X^2 + 2X. Specify the support of Z and find its density.
(1) Let X be exponential random variable with λ = 1. (a) (4 pts) Define Y = √ X. Specify the support of Y and find its density. Show all of your work and computations. (b) (6 pts) Define Z = X^2 + 2X. Specify the support of Z and find its density. Show all of your work and computat
(1) Let X be exponential random variable with λ = 1. (a) (4 pts) Define Y = √ X. Specify the support of Y and find its density. Show all of your work and computations. (b) (6 pts) Define Z = X^2 + 2X. Specify the support of Z and find its density. Show all of your work and computation
(1) Let X be exponential random variable with λ = 1. (b) (6 pts) Define Z = X^2 + 2X. Specify the support of Z and find its density. Show all of your work and computations
Suppose X~ and Y~ What is the density for X+Y? Exp(λ) We were unable to transcribe this image
Suppose X ~ G P(Y >X) if r e R+ P(Y > X) if r E Z+ amma (r , λ), Y ~ Exp(A2) and X Y. Find: a) b) Suppose X ~ G P(Y >X) if r e R+ P(Y > X) if r E Z+ amma (r , λ), Y ~ Exp(A2) and X Y. Find: a) b)
) Let Y ∼ Exp(λ). Given that Y = m, let X ∼ Pois(m). Find the mean and variance of X. estrbetrecoralcional stribution. 2. (Anderson, 10, 11) Let Y ~ Exp(A). Given that Y = m, let X ~ Pois(m). Find the mean and variance of X 3 (Anderson 10
1. Suppose that the joint density of X and Y is given by exp(-y) (1- exp(-x)), if 0 S y,0 syS oo exp(-x) (1- exp(-y)), if 0SyS ,0 oo (e,y)exp(-y) Then . The marginal density of X (and also that of Y), ·The conditional density of Y given X = x and vice versa, Cov(X, Y) . Are X and Y independent? Explain with proper justification.
1. Suppose that the joint density of X and Y is given by exp(-y) (1- exp(-x)), if 0 S y,0 syS oo exp(-x) (1- exp(-y)), if 0SyS ,0 oo (e,y)exp(-y) Then . The marginal density of X (and also that of Y), ·The conditional density of Y given X = x and vice versa, Cov(X, Y) . Are X and Y independent? Explain with proper justification. 1. Suppose that the joint density of X and Y is given by exp(-y)...
In question 5, f(x) = λ*exp(-λx), for x greater or equal to 0, and zero otherwise. 9. Let X have an exponential distribution with λ = 1 (see Question 5), and let Y = log(X). Find the probability density function of Y. Where is the density non-zero? Note that in this course, log refers to the log base e, or natural log, often symbolized In. The distribution of Y is called the (standard) Gumbel, or extreme value distribution. 2