Handwritten solution please 2.4Solve the below problem:The change in depth of a dam from one day to the next, measured (in feet) at a specificlocation, is a random variable Y with the following density function:f(y) = }4- 2

Given,f(y)=14; -2≤y≤20; elsewhere

Answered: 2.4 Solve the below problem: The change…

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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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.)
Compare a graph of the normal density function with mean of 0 and standard deviation of 1 with a graph of a normal density function with mean equal to 4 and standard deviation of 1. The graphs would: Have the same height but one would be shifted 4 units to the right. Have no horizontal displacement but one would be flatter than the other. Have no horizontal displacement but one would be steeper that the other.
Let the random variable X follow a gamma distribution with α = 4 and β = 4. If Y = X2 what is the density function of Y?
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Suppose the random variable Y has an exponential distribution with mean 2. Use the method of transformations to find the density function of U=(1/5)Y+3
An insurer's annual weather related loss, X, is a random variable with density function f(x) = 2.5 (200)2.5 / x3.5 for x >= 200 and 0 otherwise. Calculate the 30th percentiles of X. (Round to 2 decimals).
The Weibull distribution has the following density functionf(x) = (α / βα)*xα-1*e-(x/β)^α, y ≥ 0 (Shown in picture) 1. Find the cumulative distribution function and express the median as a function of the parameters α and β.2. Under what condition will this density function equal the exponential density function?3. What would be the expression for the joint distribution of 10 independent random variables with the Weibull density function? Summarize it as much as possible.
Suppose that the random variable B has the standard normal density. What is the conditional probability density function of the sum of the two roots of the quadratic equation x2 + 2Bx + 1 = 0 given that the two roots are real? KINDLY REQUEST YOU TO PROVIDE ME WITH COMPLETE SOLUTION
Let X and Y be two random variables with joint density function f(x,y) = (3 − x + 2y) / 60, for 1 < x < 3, 0 < y < 5. Determine E(Y| X = x) , the regression curve for Y as a function of X. What can know X tell you about what Y tends to be like?
ELT(Let) the joint probabilty density function of two con random variable Y and X. Please do the last three sigma x, y and PXY
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Assume that the range of X is [4.9, 5.1] mA, and assume that the probability density function of X is f(x) = 5 for 4.9 <= x <= 5.1. What is the variance?

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