5.2 If the probability density of a random variable is given byorlw o (k + 2)x³0 < x < 1f(x) =%3D0.elsewherefind the valuek and the probability that the randomvariable takes on a value1and(a) greater than -; (b) between3.4-33

f(x)=(k+2)x3 0<x<10 o/wproperities∫f(x)dx=1

2 If the probability density of a random variable is given by (k + 2)x³ 0 < x < 1 f(x) = 0. elsewhere find the value k and the probability that the random variable takes on a value 3 (a) greater than -; (b) between 1 and 3° 2.

2 If the probability density of a random variable is given by (k + 2)x³ 0 < x < 1 f(x) = 0. elsewhere find the value k and the probability that the random variable takes on a value 3 (a) greater than -; (b) between 1 and 3° 2.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Related questions

Q: The lifetime in hours of a certain component of a machine has the continuous probability density…

A: Given that, The lifetime in hours of a certain component of a machine has the continuous probability…

Q: *Ɔn average, a hospital emergency room admits 5 pcople per hour 2. and its maximum capacity is 10…

A: Let X-Number of people admitted in the hospital in an one-hour period. X~Pλ=5. Then the pmf of X is…

Q: 4.

A: 4.From the given information, the random variable X follows uniform (-1,2). The probability density…

Q: 1. Let X, X2, - ,X constitute a random sample from probability density function given by f(x;8) = 02…

A: Note: According to Bartleby an expert can solve only one question and maximum 3 subpart of the first…

Q: 6. If the probability density of X is given by for 0<x s1 1 for 1<x s 2 f(x) = 3-x for 2<x<3 2…

Q: Consider a random variable X with E[X] = 10, and X being positive. Estimate E[ln square root(X)]…

A: The Jensen's inequality is defined as: If p(x) is a convex function then E[p(x)]≥p[E(x)]. Also, a…

Q: Suppose that the lifetime X (in hours) of a certain type of flashlight battery is a random variable…

Q: 4. The function f(x) = x cos(4x) is proportional to a probability density function on the interval…

A: The mean of a probability distribution function is EX=∫-∞∞x.fx

Q: 2. Suppose that a continuous random variable X has PDF f(x) = }7 (1 – x²) -1<x<1 else

Q: Suppose that the interval between eruptions of a particular geyser can be modelled by an exponential…

A: Given.X~Exp(θ)f(x;θ)=θe-θx, x>0, θ>0.x1=32x2=10x3=28x4=60

Q: The time it takes to repair a personal computer is a random variable whose density, in hours, is…

A: Let X be a continuous random variable with probability density function fx. The expected value of…

Q: If the continuous random variable X has the probability density ( 62(1 - 2) for 0<z<1 elsewhere f(2)…

Q: 5. Suppose that X is a continuous random variable whose probability density unction is given by…

A: Given density function, f(x)=C(4x-2x2), 0<x<2 The value of C is obtained by using the…

Q: 24. Let X1, X2, ..., Xn be a random sample from a population X having the probability density…

A: Given:f(x,θ)=θxθ-1;0<x<1,θ>0.

Q: 1. If the probability density of the random variable is given by 630x (1- x) for 0<x<1 flx) =…

A: Given: The distribution given is as follows fx=630 ×x4×1-x4 0<x<1

Q: 17. The diameter of electric cable, say X, is assumed to be a continuous random variable with pdf:…

A: Given f(x)=kx(1-x) ; 0≤x<1

Q: 1. The proportion of impurities in each manufactured unit of a certain kind of chemical product is a…

A: Given, f(x;θ)=(θ+1)xθ 0<x<1,0 otherwise

Q: If the random variable Y denotes an individual's income, Pareto's law claims that P(Y > y) = k ,…

A: Reviewing the information, Given distribution is a pareto distribution such that,…

Q: Expectation of a function of random variable: Find E(πcosπx) for X uniformly distributed on [0,1].

A: Expectation of a random variable is the mean or average value of the random variable. The…

Q: 48. If two random variables x1 and x2 have the joint probability density f (x1, x2) = - (x + 2x2) }…

Q: Since the probability function of the continuous random variable X that does not take negative…

A: From the given information, f(x)=1(1+x)2 Given that the continuous random variable X that does not…

Q: 1-The probability density of an electron of hydrogen atom having r distance from the nucleus is…

Q: 6. Suppose X is a continuous random variable with a strictly positive probability density function…

A: Here are two methods of solving this probability density function…

Q: 7) Allow a continuous probability distribution to be defined as f(x) = x/2 for the range 0 sxs2. %3D…

Q: 1. Let X be an exponential random variable with mean 5. Using the technique of distribution…

A: A continues random variable X is said to folloe 'Exponential Distribution' if probability function…

Q: 8. Suppose that Y1, Y2, and Y3 denote a random sample from an population with an exponential…

A: Given that Y1, Y2 and Y3 denote a random sample from an population with an exponential distribution…

Q: Q. 4 If the probability density of a random variable is given by for 0< x < 1 elsewhere – x²) f(x) =…

A: Solution: 4. From the given information, the probability density function of X is

Q: If the probability density of a random variable is given by f( x ) = k ( 1- x² ) for 0 < x < 1 O…

A: ANSWER: For the given data,

Q: A continuous random variable X has the distribution function F(x) = 0 if x 3 The value of k is

A: Given: X has distribution function as : F(X) = 0 if X<1 = k(x-1)^4 if 1<X<3 = 1 if X >3…

Q: 4. The probability density function of the exponential distribution is given by f(x) = λe-ix A…

Q: If X is a uniformly distributed random variable between -1 and 1 (pdf of x is constant=1/(2pi)…

A: From the given information, fx=12π, -π≤X≤π Given that Y=sin(X) Consider, the distribution function…

Q: A large company has determined that the function f (x) = 3x, 0 <x<1 serves as a payroll density…

A: Answer : The value of G=0.5

Q: Then the sum n i=1 is equal to the expected value of the random variable ... (enter a correct…

A: # random variable xi with distribution function f(xi) Then sum(xi^2*f(xi)) is the expected value of…

Q: Suppose that the random variable X has the probability density function for -1 s x s 1 c(1– x²) f(x)…

Q: 11. If X has an exponential distribution with parameter 0, use the distribution function techniques…

Q: 6) Allow a continuous probability distribution to be defined as f(x) = 4x³ for the range 0 SXS1.…

Q: A continuous random variable X has probability distribution function f(x) , where f(x) = k(1 − x2)…

Q: The life lengths of two transistors in an electronic circuit is a random vector (X; Y) where X is…

A: Probability=0.3935 (b)

Q: (b) Think of one example of a random variable which is non-degenerate (i.e., takes at least two…

A: 1] Here all the odd moments identically zero. 2] Odd moments are EXn with n odd.

Q: A system for a random amount of time X (in units of months) is given by a density -x/2 xe f(x) = ;…

Q: Suppose that the interval between eruptions of a particular geyser can be modelled by an exponential…

A: “Since you have posted a question with multiple sub-parts, we will solve first three sub- parts for…

Q: 1. The proportion of impurities in each manufactured unit of a certain kind of chemical product is a…

A: Let X = the proportion of impurities in each manufactured unit of a certain kind of chemical product…

Q: 3. Suppose that X has a uniform distribution supported on [0, 1]. Find the pdf of Y = – In(X). Does…

Q: f X is a random variable that is uniformly distributed between -1 to 1, find the PDF √|X| of and pdf…

A: Solution:

Q: 3. Suppose X and Y have joint probability density function f(x,y) = {"0. 0 < x< 1,0 < y <1- x…

Q: -) Suppose X and Y are continuous random variables. The range of X is [1,3], the range of Y is [0,…

Q: 11. Suppose X1, X2, ... , Xn are i.i.d. from a distribution with pdf: f(x) = e°x-0–1 for x > e f (x)…

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

5.2 If the probability density of a random variable is given by
orlw o (k + 2)x³
0 < x < 1
f(x) =
%3D
0.
elsewhere
find the valuek and the probability that the random
variable takes on a value
1
and
(a) greater than -; (b) between
3.
4
-
3
3

Expert Solution

This question has been solved!

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

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

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

Similar questions

Suppose that a study of a certain computer system reveals that the response time, in seconds, has an exponential distribution with density curve f(x) = (1/3)e(-x/3) for x > 0 and f(x) = 0 otherwise. What is the probability that response time exceeds 5 seconds? What is the probability that response time exceeds 10 seconds?
If the probability density of X is given by f(x) =kx3(1 + 2x)6 for x > 00 elsewhere where k is an appropriate constant, find the probabilitydensity of the random variable Y = 2X 1 + 2X . Identify thedistribution of Y, and thus determine the value of k.
If the probability mass function of the variable X described in the table is. find variance Y=x^2+4x If you know that the torque is of the second order of the variable X about the origin is equal to 2.85
If the probability density of X is given by f(x) =2x−3 for x > 10 elsewherecheck whether its mean and its variance exist.
let x denotes the percentage of time out of 40 hour workweek that a call center agent is serving a client by answering phone calls, suppose that x has probability density function defin by f(x)=3x^2 for 0< x < 1. find the mean and variance of x
Suppose that Y1,Y2,Y3 denote a random sample from an exponential distribution with density function f(y) = Consider the following four estimators of θ: ?1θe−y/θ, y>0,0, otherwise. θˆ =Y, θˆ =Y1+Y2, θˆ =Y1+2Y2, θˆ =Y1+Y2+Y3 =Y ̄. 11223343 Which estimators are unbiased? Among the unbiased estimators, which has the smallest variance?