Example: Suppose that the error in the reaction temperature, in •C, for a controlled laboratory experiment is a continuous random variable X having the probability density function f(x) = 3 -1< x < 2 %3D 0, elsewhere find F (x). and use it to evaluate P(0 < X < 1).

Example: Suppose that the error in the reaction temperature, in •C, for a controlled laboratory experiment is a continuous random variable X having the probability density function f(x) = 3 -1< x < 2 %3D 0, elsewhere find F (x). and use it to evaluate P(0 < X < 1).

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: Does fxy(x,y) = $2; x> 0,y > 0,x+ y < 1 е. w. can serve as a joint probability density function of a…

A: It will serve as a joint Probability density function of a pair of continuous random variable x and…

Q: Exercise 3.3 Suppose that the probability density function of X is 0 2/3). 0,

Q: Determine the value of c that makes the function f(x,y) = cxy for 0 <x < 4 and 0 <y < 4 satisfies…

Q: Determine the conditional probability distribution of Y given that X = 1. Where the joint…

Q: -2x f(x) 0, otherwise Let X be a random variable whose probability density function is given by what…

Q: Let X be a continuous random variable with a probability density function (x) = {(6 – 3e)x² + e* 0…

A: For x≤0F(x)=∫-∞xf(x)dx=∫-∞x0dx=0For…

Q: Verify that p(x) = 3x - 4 is a probability density function on [1, oo)and calculate its mean value.

A: Probability density function:(1) p(x)≥0 (2) ∫-∞∞p(x) dx=1(1)…

Q: Let the random variable Y denote the time (in minutes) for which a customer is waiting for the…

Q: Verify that p(x) = 6x-1 is a probability density function on [1, ∞) and calculate its mean value.…

A: We are providing you the solution of last question which belongs to "Probability and Statistics",…

Q: Suppose lifetime of a particular type of old mobile, X, can be modelled by the probability density…

A: The probability density function of X is obtained below: f(x)=0.5e-0.5x;x≥0 where x is a random…

Q: The proportion of people who respond to a certain mail-order solicitation is a continuous random…

Q: Consider the probability density function x, for 0 < x < 1 f(x) = {2 - x, for 1 < x <2 0, %3D…

Q: Find a value for constant A such that x<-1 fx (x) ={ A(1- x*)cos -1<x<1 1< x is a yalid probability…

Q: if x 2 1, Let {x2 0, if x < 1. Show that f is a probability density function and that the…

A: Topic:- probability density function Note:- as per our guideline if more than one question uploaded…

Q: Find a value of k that will make f a probability density function on the indicated interval. ƒ(x) =…

Q: Determine E(X), E(X2) and V(X) if X be a continuous random variable with probability density…

A: The pdf of X is fx=3x2,0≤x≤1 EX=∫01x*fxdx=∫01x*3x2dx=3∫01x3dx=3 x4401=3144-0=34=0.75

Q: Determine the conditional probability distribution of Y given that X =1. Where the joint probability…

A: First we have to calculate the marginal density of X f(x).

Q: A lamp has two bulbs, each of a type with an average lifetime of 10 hours. The probability density…

Q: A lamp has a lightbulb with an average lifetime of 4 hours. The probability density function for the…

A: Probability density function is

Q: Determine the value of c that makes the function f (x, y) = cxy for 0 < x < 4 and 0 < y < 4…

A: The joint pdf of X and Y is given by f(x, y) = cxy , 0 < x < 4 and 0 < y < 4

Q: Example 3.11: Suppose that the error in the reaction temperature, in aC, for a controlled laboratory…

Q: Show that if the exponentially decreasing function if x 0 f(x) = LAe is a probability density…

A: Given: fx=0 ; if x<0Ae-cx ; if x≥0 For a probability density function f(x).…

Q: Suppose that the probability density function of X is 0 2/3)

A: The given probability density function of X is fx=3x2,0<x<10, otherwise

Q: Find a value of k that will make f a probability density function on the indicated interval. ƒ(x) =…

A: Find a value of k that will make f a probability density function on the indicated interval. ƒ(x) =…

Q: If the probability density function of a continuous random variable X is [.5x 0< x<2 f(x)= otherwise…

Q: Suppose that X ~ Unif[0, 1] and let Y = e^X. (a) Find the cumulative distribution function of Y .(b)…

A: In particular, the cdf and pdf of X is, Since, ex is an increasing function of x and Rx = [0, 1],…

Q: b) Find the marginal probability density function of X, fy(x).

Q: The probability density function of Y = 5X + 3 is:

A: To obtain the probability density function of Y=5X+3, we will use the transformation method.

Q: Find a value of k that will make f a probability density function on the indicated interval.ƒ(x) =…

A: Definition used- The function f(x) is a probability density function, if- i) f(x)≥0 for…

Q: Let X1, X2, ... , Xn represent a random sample from a population with a gamma(2, B) distribution,…

Q: The life (in years) of a laptop battery has a probability density function defined by P(x)=12e−x/2…

Q: The life (in years) of a laptop battery has a probability density function defined by…

Q: Find a value of k that will make f a probability density function on the indicated interval.ƒ(x) =…

A: Given probability density function is: ƒ(x) = kx2 ; Interval ; [-1, 2]

Q: Example: Suppose we want to test the hypothesis Ho: 0= 2 against H: 0= 1 on the basis of observation…

Q: The probability density function of random variable X is given by: f(x) = }K ſke*-1, -1 < x< 1; %3D…

A: To find the value of k, we will use the fact that integration of pdf f(x) over whole range of x is…

Q: Suppose that the probability density function of X is 3x 0<x<1 elsewhere Determine the P (X<1/3), P…

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

Q: 12. Suppose that the error on a reaction temperature, in °C, for a controlled laboratory experiment…

Q: What is the joint probability density function f₁,2 of Y₁ = X₁/X₂ and Y₂ = X₂?

A: We will use Jacobian method of transformation to find the joint probability of Y1 and Y2.

Q: Find a value of k that will make f a probability density function on the indicated interval.ƒ(x) =…

A: Given: ƒ(x) = kx3; [2, 4] A probability density function equals 1 for sum of all range of values.

Q: The probability density function of a continuous random variable X is given by F(2) = {*(=* = k(x² –…

Q: Example 1 Let X have the probability density function 2x ,0<x<k f(x) = {kz 0 ,e.w. For what value of…

Q: 1 A pathologist uses a microfluidic device to separate circulating tumor cells (CTCS) from a blood…

Q: 1. The proportion of people who responded to a certain mail-order solicitation is a (2(x+2) 2,0 <x<1…

A: HERE AS PER POLICY I HAVE CALCULATED FIRST MAIN QUESTION here given pdf of x

Q: Suppose lifetime of a particular type of old mobile, X, can be modelled by the probability density…

A: Given, f(x) = 0.5e-0.5x : x≥0 where x is a random variable follows exponential distribution with…

Q: Is 0.5e -0.5x a probability density function on the interval [0, ∞)? If so, what kind of proba-

A: The Exponential distribution is one of the continuous probability distribution and has one parameter…

Q: Suppose lifetime of a particular type of old mobile, X, can be modelled by the probability density…

Q: A continuous variable X has a probability density function given by p(x)=Ax^2 for 0≤x≤4, and p(x)=0…

A: Given that, A continuous variable X has a probability density function given by p(x)=Ax^2 for 0≤x≤4,…

Q: Suppose that a random variable Y has a probability density function given by Sky³e% ,y>0. f(y) = ,0.…

A: Gamma Distribution: A continuous random variable X is said to follow Gamma distribution with…

Q: Determine the value of c that makes the function f (x,y) = cxy for 0 < x < 4 and 0 < y < 4 satisfies…

Question

Solve the math and

give a explanation for which math what type of distribution we have to use especially when we have to use density function and when cumulative distribution function.

Example: Suppose that the error in the reaction temperature, in •C, for a controlled laboratory
experiment is a continuous random variable X having the probability density function
x2
f(x) = {3
-1 < x < 2
0,
elsewhere
find F(x). and use it to evaluate P(0 < X < 1).

Expression, rule, or law that gives the relationship between an independent variable and dependent variable. Some important types of functions are injective function, surjective function, polynomial function, and inverse function.

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

Similar questions

Verify that p(x) = 3x - 4 is a probability density function on [1, oo)and calculate its mean value.
Find the moment-generating function of the continuous random variable X whose probability density is given by f(x) = 1 for 0 < x < 1 0 elsewhere and use it to find μ’1,μ’2, and σ^2.
A continuous random Variable X has probability Density function defined by f(x) = 5-5x; 0
Determine E(X), E(X2) and V(X) if X be a continuous random variable with probability density function fx(x) = 3x^2 0 ≤ x ≤ 1 0 otherwise
suppose x has an exponential distribution with probability density function f(x) =2e^-2x, x>0. Then P(X>1)
Suppose that the random variables X,Y, and Z have the joint probability density function f(x,y,z) = 8xyz for 0<x<1, 0<y<1, and 0<z<1. Determine P(X<0.7).
The time, X, to infection for Eagle Flu in minutes, after coming into contact with the virus has cumulative distribution F with the following definition:F(x) = 0 for x < 1 and F(x)= (3/2)-(3/2x) for 0 ≤ x ≤ 3 a) What is the probability density function for X for 1 ≤ x ≤ 3? f(x) = .5 f(x) = (3/4x^2) f(x) =(3/2x^2) f(x) = (3/2)-(3/2x) f(x) = (3x/2x^3) b) What is the probability that X > 2? c) What is the probability X < 2 ? d) What is the probability that X > 2.5? e) What is the probability that X > 3? f) What is the probability that X > 2.5 given the X > 2? g) Calculate the 60th percentile of X. h) What is the expected value of X? i) What is the expected value of X2 j) What is the variance of X? k) What is the probability that X is more than 0.1 above its expected value?
Suppose that ƒ is a uniform joint probability density function on0 ≤ x 6 2, 0 ≤ y < 3. What is the formula for ƒ? What is theprobability that X < Y?
Let X and Y be two continuous random variables with joint probability density function f(x,y) = 2xy for 0 < x < y < 1. Find the covariance between X and Y.
Suppose that the continuous random variable X has CDF Fx(X) = {(x-2)/x , x>2 and 0, x=<2} a. Determine, and sketch, the pdf (probability density function) of X. b. Find the mean and variance of X c. Determine the pdf of the random variable Y=X^2