a)A median of a distribution of one random variable X of the discrete or continuous type is a value of X such thatPr (X 1/2 If there is only one such x, it is called the median of the distribution, Find themedian of the following: f(x) =- o < X < 0(1+x²)nb) We have continuous-type random variables X and Y having p.d.f given below:f(x, y) = 4xye-x²-y?-00 < X < o- 0 < Y < ∞=0else whereFind marginal distribution of X and Y.c) We have discrete-type random variables X and Y having p.d.f given below:f(x, y) =x=1,2,3y=1,2,34x+yFindZ=(3X-2Y) find mean and variance of Z.

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A median of a distribution of one random variable X of the discrete or continuous type is a value of X such that Pr (X

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

Question

a)
A median of a distribution of one random variable X of the discrete or continuous type is a value of X such that
Pr (X <x)< 1/2 and Pr (X <x)> 1/2 If there is only one such x, it is called the median of the distribution, Find the
median of the following: f(x) =
- o < X < 0
(1+x²)n
b) We have continuous-type random variables X and Y having p.d.f given below:
f(x, y) = 4xye-x²-y?
-00 < X < o
- 0 < Y < ∞
=0
else where
Find marginal distribution of X and Y.
c) We have discrete-type random variables X and Y having p.d.f given below:
f(x, y) =
x=1,2,3
y=1,2,3
4x+y
Find
Z=(3X-2Y) find mean and variance of Z.

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