1. The joint density for the random variables (X, Y) is given below.for 0 1,0SUSIfor clsewhere(a) Find the marginal density of X(b) Find the marginal demsity of Y(c) Finl VarX](d) Find Var(Y](e) Are X and Y statistically inslependent?() Find P(X >0.6)(R) If EXY 0.8, find the correlation between X and Y

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Answered: 1. The joint density for the random…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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6.) Suppose X is continuously uniformly distributed on [−2, 2]. Let Y = X2. What is the density function of Y? What is the expected value of Y?
For a certain psychiatric clinic suppose that the random variable X represents the total time (in minutes) that a typical patient spends in this clinic during a typical visit (where this total time is the sum of the waiting time and the treatment time), and that the random variable Y represents the waiting time (in minutes) that a typical patient spends in the waiting room before starting treatment with a psychiatrist. Further, suppose that X and Y can be assumed to follow the bivariate density function fXY(x,y)=λ2e−λx, 0<y<x, where λ > 0 is a known parameter value. (a) Find the marginal density fX(x) for the total amount of time spent at the clinic. (b) Find the conditional density for waiting time, given the total time. (c) Find P (Y > 20 | X = x), the probability a patient waits more than 20 minutes if their total clinic visit is x minutes. (Hint: you will need to consider two cases, if x < 20 and if x ≥ 20.)
1) Let X1, X2, ..., Xn be a sample of n units from a population with a probability density function f (x I θ)=θxθ-1 , 0<x<1, θ>0 . According to this: Find the estimator of moments for the parameter θ.
If X and Y are independent exponential random variables, each having parameter λ.(a) Find the joint density function of U = X + Y by using the convolution of fX and fY .(b) Find the joint density function of V = X − Y by using the method of transformation.(c) Are U and V independent?
If two random variables X1 and X2 have the joint density function given by f (x1, x2) = x1x2, 0 < x1 < 1, 0 < x2 < 2 0, otherwise Find the probability that (a) Both random variables will take on values less than 1 (b) The sum of the values taken on by the two random variables will be less than 1.
2.5.8 The random variable X measures the concentration ofethanol in a chemical solution, and the random variable Ymeasures the acidity of the solution. They have a jointprobability density function f(x, y) = A(20 - x - 2y)
Let X and Y be random variables with the joint density function f(x,y)=x+y, if x,y element of [0,1], and f(x,y)=0,elsewhere. Find the expected value of the random variable Z = 10X+14Y.
1 How can I find the distribution and density in closed form of the severity model of losses for the sum of n-losses when α = 0.5 and β = 1 (Levy)? Could someone explain to me how to calculate closed forms in general because I do not understand the concept? X_i(t) ∼ S_α(β, γ, δ; 0)
4. A continuous random variable x that can assume value between x = 2 and x = 5 has a density function given by f(x) = 2/27 (1 + x). Find a) P (x < 4) and b) P (3 < x < 4)
5.)Suppose X is continuously uniformly distributed on [1, 4]. Let Y = ln(X). What is the density function for Y ? (Include the bounds for Y .)
1-What these statistics tell you about the kurtosis of the variables:
X is an exponential random variable with λ =1 and Y is a uniform random variable defined on (0, 2). If X and Y are independent, find the PDF of Z = X-Y2

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