(1) Find the distribution of V=X₁ - X₂.
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- Suppose X1, . . . , Xn be a random sample from the Beta(θ, 1) distribution. Find the P-value for the LRT test of the hypotheses H0 : θ ≥ 1 vs H1 : θ < 1Consider a continuous random variable X such that P (−1 ≤ X ≤ 1) = 1/2. Can X be characterized by i) Uniform, and ii) Exponential distributions? If yes, find the distribution parameters which ensure the required property for X .A sample of 20 observations is taken from the normal distribution where the sample mean is 3. The normal distribution has a mean of 0 and a variance of e^beta. a)Find the estimator for the method of moments for beta and the numerical value of it?
- Suppose that X1, . . . , Xn is a random sample from the Normal distribution N (0, σ2 ) with parameter σ > 0, Find the Maximum Likelihood Estimation of σ.If Y1,...,Yn denote a random sample of sizenfrom the normal distribution with known mean μ and variance σ2= 25, find the method of moment estimator of μ.If y1, y2,..., ym be a random sample taken from a normal distribution with parameters x and n× n, then the likelihood equation is
- I need help finding the Maximum Likelihood estimator of Y1,Y2,...,Yn with a random sample size n from an exponential distribution with parameter β.For a random variable, its hazard function also referred to as the instantaneous failure rate is defined as the instantaneous risk (conditional probabilty) that an event of interest will happen in a narrow span of time duration. For a discrete random variable X, its hazard function is defined by the formula hX(k) =P(X=k+ 1|X > k) =pX(k)1−FX(k). For a Poisson distribution with λ= 4.2, find hX(k) and use R to plot the hazard function.For an initial investment of 100, an investment yields returns of Xi at the end of period i for i=1, 2 where X1 and X2 are independent normal random variables with mean 60 and variance 25. What is the probability the rate of return of this investment is greater than 10%?
- Based on a random sample of 25 units of product X, the average weight is 102 lbs., andthe sample standard deviation is 10 lbs. We would like to decide if there is enough evidenceto establish that the average weight for the population of product X is greater than 100 lbs.Assume the population is normally distributed.what is the critical value to test the claim at (alpha)= ,01?For an initial investment of 100, an investment yields returns of Xi at the end of period i for i = 1,2, where X1 and X2 are independent normal random variables with mean 60 and variance 25. What is the probability the rate of return of this investment is greater than 10 percent?It is desirable to test Ho (Null Hypothesis): Mu = 100 lb against H1: Mu <100 lb, based on the weights of a random sample of size n = 40 freight packages per truck.The population has: Image 1 For what values of X-Bar should Ho be rejected, if the probability of a type I error is alpha = 0.01?