Answered: let x be a random variable with moment…

Math

Probability

let x be a random variable with moment generating function Mx(t)=(0.6 + 0.4e^t)^20 then the variance of x is

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

Section13.3: Special Probability Density Functions

Problem 30E

See similar textbooks

Related questions

Q: Find the PSD of a stationary random process for which Auto correlation is RYx (t) 6 e- alt|

Q: Suppose a random variable X is normally distributed with mean 0 and un- known variance 0 > 0. That…

A: Hi, there! As per the multiple subparts rule, we are solving first three subparts, kindly repost the…

Q: Define gamma distribution with parameters 5 and 7 and obtain its moment generating function. Hence…

Q: a. What is probability that a randomly selected employee has a commute of less than one hour and…

A: Here given joint pdf of X and Y

Q: Suppose the distribution of the time $X$ (in hours) spent by students at a certain university on a…

A: Here, mean =50×2 =100 Variance =50×4 =200

Q: The germination rate of seeds is defined as the proportion of seeds that, when properly planted and…

A: Given information: A certain variety of grass seed has a germination rate of 0.80. The company is…

Q: Let X and Y be independent exponential random variables with the same parameter A. Define: min (X,Y)…

Q: .Define gamma distribution with parameters 5 and 7 and obtain its moment generating function. Hence…

Q: Suppose that X is a continous random variable taking value between 0 and 1 with the pdf f(x) = 2x.…

A: There is two different question So i am solving first

Q: A continuous random variable is said to have a Rayleigh distribution with parameter o if its PDF is…

A: Rayleigh distribution: A continuous random variable X is said to follow a Rayleigh distribution with…

Q: Let X, X, ..., X, be independent random variables from a distribution |(0+1)x° for 0-1 with pdf…

A: # given random variable x with pdf f(x)=(theta+1)*x^theta :0<x<1 then to find maximum…

Q: Assume that Y denotes the number of bacteria per cubic centimeter in a particular liquid and that Y…

Q: Suppose X1,..., Xm are iid gamma random variables with parameters 1 and 0 Let X, = E X; ,let W, =…

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

Q: Let x be a continuous random variable with PDF 3 x > 1 x4 fx (x) otherwise Find the mean and…

A: Given PDF is fX(x) = 3x4,x ≥ 10,otherwise

Q: The observed annual maximum runoff, X, in the Kızılırmak River has been modelled by a normal…

A: Thanks for giving opportunity to serve for bartleby students, Hey, There ! Thank you for posting…

Q: What is the pdf of the sum of two random variables each of which each is a gamma distribution with…

A: Solution

Q: X1,... , X, be a random sample from a population with PDF is Oxº -1 0 <y<1 | f(x,0)= otherwise The…

A: Option (B) correct

Q: Suppose Y is a Poisson random variable with rate A. Let X be a random variadie be such that given Y,…

A: It is given that the Y~ Poisson(λ) and X|Y=y ~ Gamma(1,Y) We have to find that the E(X) and Var(X)

Q: Suppose that the pdf for a random variable given by f(y,0) = 0y-, the method of moments estimate for…

A: Given information:

Q: ntinuous random variable

A: The PDF of uniform distribution is, fx=1b-a The moment generating function will be determined as,…

Q: Consider a random sample of a sizen taken for a population with an exponential ribution…

A: Exponential distribution: A random variable X is said to have an exponential distribution with a…

Q: Suppose the random variable X follows an Inverse Gaussian distribution with parameters u and 0. Use…

A: From the given information, the random variable X follows an Inverse Gaussian distribution with…

Q: Let X, Y be independent random variables with exponential distribution of parameter θ > 0. Are the…

A: Solution

Q: Suppose that X and Y are independent exponential random variables with parameter lambda = 1. Let Z =…

A: Exponential distribution: A random variable X is said to have a exponential distribution with a…

Q: Let X be an exponential random variable with mean 1 and X, a gamma random variable with mean 2 and…

A: Hello! As you have posted 2 different questions, we are answering the first question. In case you…

Q: Get the moment-generating function and based on it, calculate the average and variance of X

Q: Find kurtosis using quartile deviation.

A: Given : Marks : 74 29 69 66 62 53 51 44

Q: 6. Show that a gamma distribution with a > 1 has a relative maximum at x = (a- 1)ß. What happens…

A: Relative maximum =? For a gamma distribution for alpha>1

Q: Suppose that X,, X2,...,X, denotes a random sample from a Poison distribution with mean 2. Find the…

Q: The length of time, in seconds, that a computer user takes to read his or her email is distributed…

A: Given Information: Mean = 1.8 Variance= 4.0 Standard deviation is σ=4.0=2 Let X denote the length of…

Q: Find auto-correlation function of a random process whose power spectral density is given by 1+

Q: Suppose that X has the uniform distribution on the interval [0, 1]. Compute the variance of X.

A: The probability distribution function for a uniform distribution in interval a,b is given by…

Q: A researcher wants to prove that a brand X size AAA battery can last Y. Two normally distributed…

A: For 'X' batteries : sample size (n1) = 10 sample mean (x̄) = 463 sample standard deviation (Sx) =…

Q: Suppose X1,..., X, are iid gamma random variables with parameters 1 and 0 Let X, = E X; »let Wn log…

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

Q: Let X be Bernoulli random variable, find the moment generating function X and find its mean,…

A: The answer is given using the concept of the Bernoulli random variable.

Q: Let random variables X1 and X2 have the ioint pdf as

A: From the given information, fx1,x2=e-x1+x2, x1>0, x2>0 Consider,…

Q: Suppose the random variable X follows an Inverse Gaussian distribution with parameters u and 8. Use…

A: From the given information, the random variable X follows an Inverse Gaussian distribution with…

Q: Calculate the variance of a random variable X whose characteristic function is (1+ e3it)² f(t) = 4

A: We have given that the characteristics function of random variable X and we have to calculate the…

Q: Suppose that X, Y and Z are statistically independent random variables, each of them with a x²(2)…

A: Result: if X~χ2(n) Mx(t)=(1-2t)-n/2 If X and Y are independent then E(XY)=E(X)E(Y)

Q: Let the continuous random variable X denote the distance in micrometers from the start of a track on…

A: Exponential distribution: A continuous r.v. X taking non-negative values is said to follow an…

Q: 9. A number of persons are measured for their heights x, weights y and chest expansion z and product…

Q: 5. Let (x1, 82, .., En) be a random sample from the distribution f(x) = Ax^-1; 0 0. Find the moment…

Q: Suppose the lifespan (in months) of a smartphone battery can be modeled as a continuous random…

A: Given,F(X)=1-e-x3 ; x≥0

Q: Explain Functions of Normally and Log-normally Distributed Random Variables

Q: Suppose that n observations are chosen at random from a continuous pdf fY(y). What is the…

A: Suppose that n observations are chosen at random from a continuous distribution with a PDF fY(y)…

Question

let x be a random variable with moment generating function
Mx(t)=(0.6 + 0.4e^t)^20
then the variance of x is

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 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Multivariate Distributions and Functions of Random Variables$

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

let X and Y be independent standard normal random variables. Determine the pdf of W = X^2 + Y^2. Find the mean and the variance of U= (1/2)W
Y, = XB + ɛ, Show that the model variance in model Yi unbiased estimator of
Find the variance of the random variable X with a PDF given by 3x2 S* if - 1< x< 1, f(x) = 2 otherwise. Submit your answer in fractional form.
Show that the variance of a geometric random variable X; is given by V ar(X) = q/p^2 .
Let Y be a random variable with pdf f(y)= (1/18)(y^3−1) for 1<y<3.(a) Calculate P (Y > 2.5).(b) Calculate the variance of Y .
Q5 Find the variance for the PDF px(x) = e-«/2, x > 0.
Let Y be a random variable with the mgfM(t) = .35e^(−4t) + .1 + .25e^(2t) + .3e^(4t).(a) What is the pmf of Y?(b) Calculate the variance of Y directly from the pmf you determined in part (a).(c) Calculate E[Y^4] directly from the mgf.
Suppose that f(x) = 0.125x for 0 < x < 4 Determine the mean and the variance of X.
Let X be a continuous random variable with PDF 3 x > 1 x4 fx(x) = otherwise Find the mean and variance of x.
Show that variance o? = (x²) – ((x))²
Suppose that f (x) = e=* for 0 < x Determine the mean and variance of the random variable.
calculate the variance of g(X) =X^2+2, where X is the random variable with probability distribution : x=0,1,2,3; f(x) = 0.1, 0.2, 0.4,0.3 . a. 19.65 b. 26.28 c. 10.65 d. 11.65 e. 14.65