Problem 3. Transformation of a Random Variable. Let X N(0, 1). What is the p.d.f. of Y = = fx(X)? (note that here we are treating fx as a function, so the right-hand-side is a function of a random variable "capital X", not lowercase. In other words, as written Y is a transformation of X).

Problem 3. Transformation of a Random Variable. Let X N(0, 1). What is the p.d.f. of Y = = fx(X)? (note that here we are treating fx as a function, so the right-hand-side is a function of a random variable "capital X", not lowercase. In other words, as written Y is a transformation of X).

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter13: Probability And Calculus

Section13.CR: Chapter 13 Review

Problem 43CR

See similar textbooks

Related questions

Q: [Q4] Determine the following probabilities for the standard normal random variable Z: (a) P(Z 1.45)

A: Z be a standard normal random variable with mean μ = 0 and standard deviation σ = 1

Q: P 1) a) Find the value of zo such that P(Z > %o) = 0.5. ERN b) Find the value of zo such that P(Z…

A: (a) P(Z>Zo)=0.5(b)P(Z <Zo)=0.8643(c)P(−Zo <Z <Zo)=0.90

Q: Suppose that the random variables Y1 and Y2 have joint probability distribution function. f(y1,…

A: The joint probability density function is given as,The marginal density function of y1 is,The…

Q: The mean percent of childhood asthma prevalence in 43 cities is 2.43%. A random sample of 34 of…

Q: A clinical trial was conducted to test the effectiveness of a drug for treating insomnia in older…

Q: 6.5 Let X have the uniform distribution on [0,1]. That is, it has density f(x) = 1 for 0≤x≤ 1, and…

Q: Once an individual has been infected with a certain disease, let X represent the time (days) that…

A: Let f be a pdf ; x>=0= 0 ; x<0

Q: 6. Suppose that P(E)=0.61, P(F) = 0.43, and P(EF) = 0.27. Find the following:

A: 6) Given,P(E) = 0.61P(F) = 0.43And 0.27Using formula,

Q: A fair coin is tossed 17 times. What is the probability of getting exactly 14 tails?

A: A fair coin is tossed 17 times. The objective is to find the probability of getting exactly 14…

Q: Industry A is responsible for producing 60% of cements in Lebanon while Industry B produces the…

Q: Given a function f(y) {cye-2y, 04) Find the distribution function

Q: ume a member is selected at random from the population represented by the graph. Find the ability…

A: Mean ==270Standard Deviation==11Z score=

Q: The number of tickets issued by a meter reader for parking- meter violations can be modeled by a…

A: Poisson process with parameter of 6 per hour

Q: Help me please: Let X be a random variable that is uniformly distributed over the interval [0, 2π]…

Q: Car Owners Truck Owners 0.25 O 0.625 O 0.375 O 0.294 <20 Miles per gallon O 0.158 200 500 20 miles…

A: The frequency table shows that:There are 500 truck owners who get less than 20 miles per gallon…

Q: A pizza restaurant sells two different crusts (regular and thin-crust) and three different toppings…

A: 1.Types of Crusts:Regular crustThin crust2. Types of Toppings:PepperoniSausageBell peppersGiven…

Q: day. Which probability distribution is most nearly appropriate to describe the number of dog bite…

A: It is assumed that the random variable represents the number of dog bite victims.

Q: 1. Find n(AUB) for each pair of sets described. a) n(A)-10, n(B)-8, a(4B)-4 b) n(A)-7, n(B)-12. ACB

A: Given that

Q: X and Y are independent random variables, -{ex. y20 x>0 0, others' 0, others Let U=X+Y, V=X/(X+Y).…

A: We have given, and are independent random variables. &

Q: A pair of fair dice are rolled. What is the probability of their sum being at most 5?

Q: The population mean and standard deviation are given below. Find the required probability and…

A: sample size(n)=75Mean()=223standard deviation()=5.9

Q: builtrite has calculated average weekly daily sales to be 80000 with a standard deviation of 12000.…

A: Mean()=80000standard deviation()=12000 one store manager made a bet with another store manager that…

Q: 6. Ten cards are dealt from a standard deck. (a) What is the expected number of queens? (b) What is…

Q: In the following problem, check that it is appropriate to use the normal approximation to the…

Q: In the video "How many ways are there to reorder the word MISSISSIPPI?" by Dr. Trefor Bazett, Dr.…

A: NoteAs per our policy, we'll answer the first three subparts. Kindly repost this question and…

Q: Suppose that a department contains 9 women and 15 men. How many ways are there to form a committee…

A: Given:Total women = 9Total men = 15Total committee members required = 7Condition: The committee must…

Q: A research institute reports that 73% of workers reported that they and/or their spouse had saved…

A: From the information, given thatLet X denotes the number of workers and their spouses have saved…

Q: A diagnostic test for a certain disease is applied to n individuals known to not have the disease.…

A: Let X= the number among the n test results that are positive.X is the number of false positives).…

Q: Problem 10-17 (Static) An office employs several clerks who create documents and has one operator…

A: In this system population is infinite, arrivals are poisson distributed and service time is…

Q: wo random variables, x and y, with values 0, 1, or 2, have the joint probability mass fun n in the…

A: We have a joint probability mass function of two random variable X and Y is given as…

Q: a biscuit tin contains 8 bourbons and some digestives. there are n biscuits in total in the tin. Roy…

Q: Candidate A and Candidate B have a hotly contested race for Florida's electoral votes. Suppose each…

A: P=0.5003We have 8084000 voters in Florida

Q: Problem 4: A finite state machine has 3 states, labeled {1, 2, 3}. The input of this state machine…

A: Given that a finite state machine has 3 states, labeled {1, 2, 3}. The input of this state machine…

Q: Consider the following transition probability matrix: [0.6 0.2 0.2 P= 0.3 0.4 0.3 0.0 0.3 0.7 a.…

A: transition probability matrix is given:

Q: Q 4.4. An individual picked at random from a population has a propensity to have accidents that is…

A: Given that the random variable Y has the gamma distribution with shape parameter and rate parameter…

Q: raffic engineers are investigating the high rate of fatal accidents at a lighted city intersection.…

A: 10% of the cars that are within 200 feet of the intersection when the light turns red pass through…

Q: Given two dependent random samples with the following results: Population 1 48 29 32 29 38 31 28…

A: The formula for the Confidence interval for paired differences between the mean is:

Q: Question 1 how many ways girls be selected for the end and three 8 boys Can from 10 boys and 5 girls…

A: Number of boys = 10Number of girls = 5

Q: A chemical system that results from a chemical reaction has two important components among others in…

A: Hello! As you have posted more than 3 sub-parts, we are answering the first 3 sub-parts. In case…

Q: A survey of 249 UNLV students regarding the mode of transportation they use to commute to the campus…

A: A survey of 249 UNLV students regarding the mode of transportation they use to commute to the campus…

Q: 5) The joint probability density function of X and Y is: y), 0, fxy(x, y) = {K (x + a) Find…

A: Let X and Y have joint pdf

Q: Let the probability of success on a Bernoulli trial be 0.30. a. In five Bernoulli trials, what is…

A: The probability of success on a Bernoulli trial is 0.30.

Q: Let X₁/Xn ~ N( M₂ ~ ² ) what is MLE for M₂ 2²

A: X~N(μ,σ2)

Q: A machine can be in one of four states: ‘running smoothly’ (state 1), ‘running but needs adjustment’…

A: Given that to be the state of the machine on the morning of day for .

Q: Find the z-score that has 3.851% of the distribution's area to its left. The Z-score is (Round to…

A: The formula of the Z-score is,Where,X denotes the raw data point, µ denotes the population mean,σ…

Q: There are 5, 673 students enrolled at the University of New Mexico Suppose I as each one of them to…

A: Given that there are 5673 students.Suppose I ask each one of them to pick a number between 1 and…

Q: Suppose a battery has a useful life described by the exponential distribution with a mean of 500…

A: Mean=500 days X is the exponential distribution with mean= 500 days

Q: A bowl contains 10 chips where only one is red. Draw chips from the bowl without replacement until…

A: We are given that a bowl contains 10 chips and only one is red. Draw chips from the bowl without…

Q: Question 1 The mean number of citizens voting in one of the provinces on the election day is 10 per…

A: As per our guidelines we are supposed to answer only one question kindly post the remaining…

Q: Once an individual has been infected with a certain disease, let X represent the time (days) that…

A: The pdf of the Weibull distribution is,The values of the parameter are , and .

Question

Please answer asap, dont need to find numerical value just an expression.

Thank You

f_X refers to the standard p.d.f., so

f_X(x)=(1/sqrt(2pi)) e^{-x^2/2}

Problem 3. Transformation of a Random Variable. Let X~ N(0, 1). What is the p.d.f.
of Y = fx(X)? (note that here we are treating fx as a function, so the right-hand-side is a
function of a random variable “capital X”, not lowercase. In other words, as written Y is a
transformation of X).

Definition Definition Probability of occurrence of a continuous random variable within a specified range. When the value of a random variable, Y, is evaluated at a point Y=y, then the probability distribution function gives the probability that Y will take a value less than or equal to y. The probability distribution function formula for random Variable Y following the normal distribution is: F(y) = P (Y ≤ y) The value of probability distribution function for random variable lies between 0 and 1.

Expert Solution