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.

"Since you have asked multiple questions, we will solve the first question for you. If you want any…

Answered: A median of a distribution of one…

Math

Statistics

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

Problem 1P

See similar textbooks

Related questions

Q: Find marginal distributions P(x) and P(y)

A: The objective is to construct the marginal distribution of P(x) &P(y) Given that the joint…

Q: The distribution of the random variable X is determined by the function: f(x) = ((x-1)2)/c ; for…

Q: Suppose that a continuous random variable X follows a uniform distribution over {-4, 4]. (a) Find…

Q: Let x1,x2,...x n be an iid sample with pdf f(x|0)=0X (® -1) Osxs1,0>0 Find the MLE of 0.

Q: 2. Let X, Y be two independent random variables satisfying standard normal distributions, then the…

A: Given: Let X,Y be two independent random variables satisfying standard normal distributions. We need…

Q: Let X be a continuous random variable. Prove Var(X) > 0.

A: Solution:- Given that let X be a continuous random and prove that Var(X) > 0.

Q: If the variance of a poisson variate is 3. Find the probability that X = 0 i) i) ii) 0<x<3 18x<4

Q: Uniform distribution Unif (-8.0] having paf fix;o) = 0 - xE l-8. e] and zero elsewhere. hat is the…

Q: Suppose that the random variable x f (x) = { Set-2 0, for x < 2 el sewhere Determine the 75th…

A: Solution: From the given information, the probability density function of X is

Q: Let the joint pdf for the continuous random variables X and Y be: f(x,y) = { 4xy; 0<x<1, 0<y<1…

A: Let the joint pdf for the continuous random variables X and Y be:f(x,y) = { 4 xy; 0<x<1,…

Q: Let X be a continuous random variable that is normally distributed with mean, µu = 15 and standard…

Q: Let X be the continuous random variable which is the age of a first-year university student selected…

Q: Consider the three functions I. f(x)= {1-x if 0 < x < 2 {0 otherwise II. f(x)= {1+x if 0 < x < 2 {0…

A: f(x) can be probability distribution function if integration|xf(x)dx = 1 It means the total…

Q: Determine the distribution of Xn for the following

A: Given that X1, X2, .....X15 are random sample from the Poisson distribution with parameter λ.…

Q: 01: If the random variable (x) has a uniform distribution on the interval [0,6]. Find: a) P(1 < x <…

Q: 6. Given a continuous uniform distribution, show that A+B (a) μ = and 2 (b) 02: (B-A)² = 12

A: The objective of this question is to derive the formulas for the mean (μ) and variance (σ²) of a…

Q: 3. Let X be a random variable with distribution function P(X ≤x} = { 0 x 1 if x ≤ 0, if 0 1. Let F…

Q: Find Pr (0 < X1 <1/3,0 < X2 < ½) if the random variables X1and X2have the joint p.d.f. S(X1, X2) =…

A: From the given information, fx1, x2=4X1(!-X2), 0<X1<1, 0<X2<1 Consider, P0<X1<1/3,…

Q: Let X1,..., X, be a random sample from a two-parameter Weibull distribution with pdf x > 0 f(x) = 0,…

A: It is an important part of statistics. It is widely used.

Q: Suppose that the random variable X has the continuous uniform distribution on the interval [0,1]. A…

A: It is given that X~U(0, 1).

Q: For the continuous probability functionf(x) = Kx when x20 find

Q: if x be a random variable belong to geometric distribution with mean= 3 then p(x-D2) is

A: It is given that mean (1/p) is 3.

Q: 3 Let X be a random variable with f(x)= 25x53. 4 0 otherwise a) Find and graph F(x). Find the value…

A: The provided function is, fx=34 0≤x≤114 2≤x≤30 otherwise

Q: a) Find mean and variance of distribution by using M.G.F technique.(1 – p)* p

A: Note: Hey there! Thank you for the question. As you have posted multiple questions, we have helped…

Q: (a) P(2 < Xs 5), (b) P(3 < X s 7), and (c) P(X 2 6). *

Q: Let x be the mean of random sample size (n) from distribution N(u, 10). Such as P(x- 1<u<x+1)%3 0.90…

A: Given that, Population variance σ2=10 Population standard deviation σ=10=3.1623 Margin of error E=1…

Q: The continuous random variable T represents the time in hours that students spend on homework. The…

Q: The cumulative distribution function of a discrete random variable X 0, x< -2 1/5, F(X) = 7/10, -2…

Q: Calculate the Average and the variance

Q: et X(1) 0. a) Show that X and X) - X() are independent for any s>r. p) Find the distribution of…

Q: Suppose X - Fm,n- a) Find the distribution of 1/X. b) Find the distribution of (m/n)X Y = 1+ (m/n)X…

A: Given, X~Fm,n. The pdf of F-distribution is, f(x)=mnm2.xm2-1B(m2,n2) (1+mnx)m+n2

Q: Let X; € {1,2, 3, ...} be the number of days until relapse for patient i who is diagnosed with…

A: The following figure is as, Blue : Posterior Green : Likelihood Red : Prior

Q: Assume that X donotos the continuous random varlable with probability distribution of y & (A) and…

A: Basic probability

Q: À continuous random variableX has a probability density function (p.d.f) given by f(X)=K(10-X)(X-40)…

Q: Let X represent a continuous random variable with a Uniform distribution over the interval from 0 to…

A: Hey there! Thank you for posting the question. Since your question has more than 3 parts, we are…

Concept explainers

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.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 1 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Point Estimation, Limit Theorems, Approximations, and Bounds$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.

Similar questions

Areas under normal distribution curves can be used calculate probabilities of many random variables in the natural and social sciences. The graph of the Standard Normal Curve, with a mean of 0 and a standard deviation of 1 is given below, and its function is given by 1 f(x) = √2T e 1 The integral of e dx would be used to calculate the probability of an event that occurs √2T -1.5 between -1.5 to 1.5 standard deviations from the mean. (-1.5, 0.13) 1 Unfortunately, √2π -1.5 methods to approximate the values. 1.5 -1.5 1.5 (-1, 0.24) Using Simpson's Rule, (-0.5, 0.35) e dx has no proper closed form antiderivative, so we must use numerical 1.5 -1.5 1-0.5 -0-2 Using the Midpoint Rule with three rectangles of equal width, dx 0 Using the Trapezoidal Rule with six trapezoids of equal width, (0, 0.4) 0.5 Round answers to 4 decimal places when appropriate. (0.5, 0.35) (1, 0.24) 1.5 Ibe 1.5 1.5 [ 13 e-t de = \ е 1.5 e-2 е dx (1.5, 0.13)
Let A1, A2, . . . , A100 be a random sample from a uniform distribution on the interval(0,1). Let B = A1 + A2 + . . . + A100. 1. Let A¯ = B/100. Find P(2 < A¯ < 2.15).
A continuous random variable X has probability distribution function f(x) , wheref(x) = k(1 − x2) for − 1 < ? < 1. Calculate the P(X < 0)?
Suppose X is a random variable of uniform distribution between 1 and 7. Find E(X)
Let random sample of n observations from each of the distributions: a. Poisson distribution with parameter θ. b. f(x, θ) = (1/ θ) e-x/θ , 0 < x. In each case find the Minimum Variance Estimator of θ and prove its efficiency.
Give the answer for question 4
Suppose the random variable X has a continuous uniform distribution on the interval (20,80). What is P(X > 52 | X > 28)? (Give your response to at least 3 decimal places
Q.6 (a) Write the gamma distribution for a random variable X denoted by X~F(a, B); its mean, variance and moment generating function (No derivation is required). (b) What is the relationship between gamma distribution and chi-square distribution?
Let X be a random variable with a uniform distribution over the interval [-2 , 4]. Determine the mean of X. The answer should be a number rounded to five decimal places
X is a normally distributed random variable with mean 72 and standard deviation 22. Use calculator to find the probability indicated. a) P(78<X<127) b) P(60<X<90) c) P(X=80) *continuous
Let X be a continuous random variable that follows a uniform distribution over the interval (-3, 7]. Find the following. a. E(X) b. P(X=6) c. P(X<5) d. P(X|<4)