Given that the moment-generating function for the chi-square random variable is derived by (t) (1– 2t)2. Differentiate this mgf to find the mean and variance of the chi-square istribution.

Q: Let us consider a discrete random variable having the pmf given by, PX(k) = { (1/3) , k = 1   (2/3)…

A: The moment generating function of x is given by: Mxs=EesX=13es+23e2s+0e3sMxs=13es+23e2s

Q: There is a p(x1) = 0.4 probability to observe x1 = 10 and p(x2) = 0.6 probability to observe  x2 =…

A: We have given that  X 10 5 P(X) 0.4 0.6

Q: Derive the variance of the Student's t distribution using the definition Var (X) = ELX²] - Ex)²

A: t distribution: Let us assume X is a random variable following standard normal distribution and Y is…

Q: The table below shows a sample of waiting times​ (in days) for a heart transplant for two age…

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

Q: Find the least square estimate for beta (the slope) given that its y-intercept is 0. Y_i = BetaX_i +…

A: Step 1:

Q: Suppose that average male weight in the US is 175 pounds with a standard deviation of 25 pounds.…

A: It is given that population mean µ=175 pounds, population standard deviation σ=25 pounds. Sample…

Q: Let X1,...,Xn be a sample from normal with mean theta and variance 1. Construct an unbiased…

A: We are given a random sample X1, X2, ..., Xn from a normal distribution with mean θ and variance 1.…

Q: The data shown in the table represent the measurements of 10-kΩ resistors (in kΩ) produced from four…

A: Given Data :   Machine 1 Machine 2 Machine 3 Machine 4   9.9823 10.0269 9.8961 9.9894…

Q: Suppose a continuous random variable X pdf constant from 0 to 7.516, where the pdf is zero…

A: Suppose a continuous random variable X pdf constant from 0 to 7.516, where the pdf is zero…

Q: A manufacturer of sunflower oil uses machines to distribute liquid ingredients into bottles that…

A: Provided information is, a manufacturer of sunflower oil uses machines to distribute liquid…

Q: Let Y₁, Y2, ..., Yn be a random sample from a population with a Gamma distribution with parameters a…

A:

Q: Q2) Let X, X X. iid N(H,0), be a random sample from the normal population where u is assumed known.…

A:

Q: "What is the correlation coefficient for this condition? X is the voltage across a resistor, Y is…

A: We have given that the statement about to the correlation condition of X and Y.   Note: According to…

Q: A manufacturer of cigarettes wishes to test the claim that the variance of the nicotine content of…

A: Given, The degrees of freedom is obtained as- The hypothesis to be tested here is- This is a…

Q: table below shows a sample of waiting umes (in heart transplant two age groups. At a- that the…

A: Given data, 18-34 35-49 156 211 172 194 166 209 170 210 163 196   210   200…

Q: Derive formulas for the mean and variance of a Poisson random variable with parameter λ using its…

A: The objective is to find the formula for the mean and variance of a poison random variable with the…

Q: Suppose that the number of customer that enter a bank in an hour is a Poisson random variable, and…

A: Let X be poison random variable P(X=0)=0.05 variance of X=?

Q: PSOHS had administered an IQ level test to 15 randomly selected G11 students. And the result they…

A: From the provided information, Sample size (n) = 15 Sample mean (x̄) = 110 Standard variance (s2) =…

Q: The number of ice creams sold per hour from Mr Fishy’s van is observed to be a Poisson random…

A: X be the distribution of the number of ice creams sold per hour which follows a Poisson distribution…

Q: Let X₁, X2, X, be normal random variables with mean and variance 2. What are the method of moments…

A: X~N(μ,σ2)

Q: The number of clients a store has during a week is Poisson distributed with mean A = 25. The amount…

A: The moment generating function is, ϕt=e1000t+250t2 Mean: Et=ddtϕt   by putting t=0…

Q: The following is the summary of a sample data collected on n=10 students on x= # of hours spent…

A: We have to calculate MSE for regression of y on x

Q: Our random variable X has a beta distribution with a = 7 and B = 3. %3D What is the variance of the…

A:

Q: Let's take XI, X2 ... Хой a radom sample of distribution defined in from the uniform (0, 0+1). Is…

A:

Q: Use the result of Exercise 45 to show that, if n independent random variables Xi have normal…

A: The mean is calculated as follows:

Q: The number of cracks that need repair in a section of interstate highway follows a Poisson…

A: For a discrete random variable X ~P(m) the pmf is given as :   P(X=x) = e-mmxx!      , x=0,1,2,3,...…

Q: how that the variance of a geometric random variable X; is given by V ar(X) = q/p^2 .

A:

Q: Y, = XB + ɛ, Show that the model variance in model Yi unbiased estimator of

A:

Q: Statistics Question

A: Given that : The number of cell phone in the household Number of household 0 211 1 288 2…

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: A random variable X has only two values a and b with P(X = a) = p , P(X = b) = q (p + q = 1). Find…

A:

Q: Find the variance of the time to failure for two identical units, each with a failure rate 1, placed…

A:

Q: Let X and Y be independent random variables. Suppose X has variance 2 and let Y have variance 5.…

A: Given Data: Var(X)=2 Var(Y)=5

Q: a) Find the value of ‘*’ and Find the expected category of hurricane to make landfall, E(X).   What…

A: xP(X=x)10.4120.3430.1340.075*

Q: Let xy X2 ..., Xn be a random sample from a Poisson distribution with parameter A. Find ML estimator…

A: ANSWER:  For the given data,

Q: The time at which a bus arrives at a station is uniform over an interval (a,b) with mean 2:00 pm and…

A:

Q: The data shown in the table represent the measurements of 10-kΩ resistors (in kΩ) produced from five…

A: Given: