6) Assume that there is a continuous random variable X with the following probability density function. f&) = {°C Sc(1 – x4), 0, 0 < x<1 otherwise a) Find the constant c, such that f(x) becomes a pdf. b) Find the mean (expected value) of the random variable x. c) p(1/3

6) Assume that there is a continuous random variable X with the following probability density function. f&) = {°C Sc(1 – x4), 0, 0 < x<1 otherwise a) Find the constant c, such that f(x) becomes a pdf. b) Find the mean (expected value) of the random variable x. c) p(1/3

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.6: Applications And The Perron-frobenius Theorem

Problem 24EQ

See similar textbooks

Related questions

Q: Q.3 The probability density function for a continuous random variable X is (a + bx²; 0 < x< 1, fx(x)…

A: NOTE-By bartleby rules, only first question has been answered. As per given by the question, there…

Q: a. Explain the difference between discrete and continues probability distribution and give an…

A: Dear students as per guidelines we answer the first only. Please post other question in a subparts.…

Q: b. Let X be a continuous random variable with probability density function for 0 <x < 1 for 1 <x< 3…

A: Givenf(x)=a for 0≤x≤1b for 1≤x≤30 otherwise

Q: (ii) Let the random variable, y have probability density function, kye-0.5y f(t) = { , y 2 0…

A: Given: Probability density function: ft=kye-0.5y , y≥00 , elsewhere The…

Q: Let X be a Geometric random variable with parameter p = 1/4. Find E(4X + 1)² and V(3 + 2X). Two fair…

Q: Q. 4 Let X and Y be two continuous random variables with following joint probability density…

A: Hello. Since your question has multiple sub-parts, we will solve first three sub-parts for you. If…

Q: Suppose that X,Y are jointly continuous random variables with the joint probability density function…

Q: 9. Let the joint probability density function of random variables X and Y be given f(x, y) = 2 0 if…

A: The joint density function of random variables X and Y is f(x,y)=2if 0≤y≤x≤10elsewhere

Q: Q.3 The probability density function for a continuous random variable X is = {a + bx²; 0<x< 1, 0; }"…

A: Hi! Thank you for the question, As per the honor code, we are allowed to answer three sub-parts at a…

Q: Let P(A) = r and P(B) = s with AN B= p. Then P(A\B) equals Select one: а. 1 b. 1-5 C. 0 d. r

A: NOTE: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: (f) The random variable X has the following probability density function: (3x + 3)(x+3)/16 for 00.75…

A: Find P(X>0.75|X>0.5)=? Cov(X+3,(X+3)-1)=?

Q: 2- Let X be a random variable with the following probability density function: 4e-4x lo x >0 f(x) =…

Q: Let X be a continuous random variable with pdf 0 <x <1 1<x < 2 2 < x < 3 ax a f(x) = -ax + 3a…

A: (i) As if f(x) is a pdf then ∫-∞∞f(x)dx = 1⇒ ∫01axdx + ∫12adx + ∫23(-ax + 3a)dx = 1⇒ ax2201 + ax12 +…

Q: Let X₁, X2, X3,...,Xn be a random sample of n from population X distributed with the following…

Q: A continuous random variable X has a probability density function given by dF = ka?e-dx,0 <x < 0o.…

Q: b) The probability density function of random variable X is given as: S(x) = {4 - Bx if 0 <x<1…

Q: Suppose X and Y have joint probability density function [C(x²+y²), _if0<x<y<1, otherwise. f(x, y) =…

A: The formula to calculate the expected value of x is,The formula to calculate variance of x is,

Q: Suppose that the random variable X has the probability density function flW) = 0 ( (1- x²) for - 1s…

A: Given p.d.f : f ( x ) = ∫-11 c ( 1 - x2 ) dx for -1 ≤ x ≤ 1 o…

Q: 1 (a) ƒ (kx) = 2x+1_2²²₂ = - 2*, x = 1, 2, ..., N, and zero elsewhere (b) f(x)=p(1-p)*, x=0,1, 2,…

A: As per bartleby guidelines we can solve only first three subparts and rest can be reposted # To…

Q: If the random variable Y has the following probability density function f(G) = }5 ,0 <y<5 (0…

Q: Q.3 The probability density function for a continuous random variable X is fe(8) = {* *o; Sa + bx²;…

A: Note: Since it is very long question. In each question there are multiple sub parts. I am answeing…

Q: Find theprobabilities that it will take on a value (1) between 1 and 3 (2) greater than 0.5.

Q: Find E[x] , P[A] , px|A(X) and E [x | A]. b) Let y=x2.Find E[y] and Var[y] .

Q: Q.3 The probability density function for a continuous random variable X is Sa + bx²; 0 s< x< 1,…

A: Hi! Thank you for the question, As per the honor code, we are allowed to answer three sub-parts at a…

Q: Q2 (a) i Determine the constant amount of C so that the random variable X is a valid probability…

Q: - Let x be a random variable with probability density function, f(x) = C (1- x2), -1 < x < 1 and 'O'…

Q: 4 The continuous random variable X has cumulative distribution function: x 3 Find: a P(X> 2.4) b the…

A: I solved exactly 3 subpart of given question... because of bartleby policy. If you want more please…

Q: 2. A discrete random variable X has probability density function of the form (c(8 – x) for x = 0, 1,…

Q: 7. Let X be a continuous random variable with probability density function given by Se-(z-z0) x > x0…

A: Let X be the continuous random variable with probability density function is, f(x) = { e^-(x-x0)…

Q: Q.3 The probability density function for a continu random variable X is Sa+ bx2; 0< x< 1, fx (x) :…

A: NOTE : As per bartleby guidelines for more than one question asked only one is to be answered…

Q: cumulative distribution function Fx,y(x,y);

A: Let X and Y be two random variables with the following joint Probability density Function…

Q: Q1. The cumulative distribution function of the random variable X is F(x) = 0, (+1)², 1- (1-2)², 1,…

A: Let X be the random variable having cumulative distribution function

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

6)
Assume that there is a continuous random variable X with the following
probability density function.
Sc(1 – x*),
0,
0 <x<1
f(x) =
otherwise
a) Find the constant c, such that f(x) becomes a pdf.
b) Find the mean (expected value) of the random variable x.
c) p(1/3<x<1/2)
d) p(x<0.5)

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 2 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, probability and related others by exploring similar questions and additional content below.

Similar questions

B) Let X and Y be discrete random variables with joint probability function 2-y+1 9 for x = 1,2 and y = 1, 2 p(x, y) otherwise Calculate E(Y/X).
Suppose X is a continuous random variable defined on (-∞, ∞) and its probability density is of the form 1 fx (t) = exp(-1) 4 What's b, E(X), and Var(X)? please show your derivations in details.
Suppose that X, and X2 are aiscrete random variables with joint pdf of the form f(x1, x2) = c(x, + x2), x1 = 0,1,2; x2 = 0,1,2
Let X and Y be two jointly continuous random variables. Let Z = X² + Y². Show that F2(=) = L Fxr(V=- yř 19) – Fxy(-v/= = y"l»)] fv (w) dy .
Let X1, X2,... , Xn be independent Exp(A) random variables. Let Y = X(1)min{X1, X2, ... , Xn}. Show that Y follows Exp(nA) dis- tribution. Hint: Find the pdf of Y
6) The joint probability density function of two random variables, X and Y is given by 1² – 2pxy + y² 202 - 00
Let X and Y be random variables with common range { 1, 2 } and such that P(X = 1) = 0.39, P( Y = 1) = 0.46 and P( X = 1, Y= 1) = 0.13 Then P( X = 1, Y = 2) = Preview P(X= 2, Y = 1) = | P(X= 2, Y = 2)= Preview Preview
Let X and Y be random variables having the same distribution. Show that Cov(X +Y, X – Y) = 0.
2. Let X be a random variable with density function ) = √(2x² - + f(x) = Find the expected value of g(x) = 2X+1. 8x2 +5x + 6), 1 < x < 2, 0, elsewhere
Let X1, X2, X3 be independent Exp()-distributed random vairables. Determine the pdf of X(1)X(3)
-) Suppose X and Y are continuous random variables. The range of X is [1,3], the range of Y is [0, 1]. The joint pdf of X and Y be given by f(x, y) = 2xy³ - 2y³. Verify if X and Y independent random variables.
Plz do fast