5. Show that for a normal distribution with mean u and variance o', the central moments satisfy the relation. ika =0 and u = (2K -1)ux-2ơ². !!
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- Suppose X1, ..., Xn have been randomly sampled from a normal distribution with mean 0 and unknown variance sigma^2, and let U = c * i=1 -> n summation (X_ i)^2 , where c is a constant. Find the value of c that minimises the Mean Squared Error (MSE)If the variance of a continuous random variable X with pdf f(x) is noted as V(X), what is its standard deviation?Records for the last 15 years have shown that the average rainfall in a certain region of the country, for the month of March, to be 1.20 inches, with s = 0.45 inches. A second region had an average rainfall of 1.35 inches, with s = 0.54. estimate the difference of the true average rainfalls in those two regions as a 95% C.I. with the assumption of normal populations and unequal variances.
- 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.Let X be normally distributed with mean 3 and standard deviation 2, and let Y be normally distributed with mean 8 and standard deviation 1. Suppose (X, Y ) have a bivariate normal distribution with Cov(X, Y ) = 1.5. What is P(X > Y )?Consider the continuous random variable X = the weight in pounds of a randomly selected newborn baby born in the United States last year. Suppose that X can be modeled with a normal distribution with mean μ = 7.57 and standard deviation σ= 1.26. If the standard deviation were σ = 1.06 instead, how would that change the graph of the pdf of X?
- Suppose that Z given Y = y has a normal dlistibution with mean zero and variance y^2 and that Y has a x^2 distribution with v degrees of freedom. find the variance of W = Z/sqrt(Y).Let X be a continuous random variable with mean μ and standard deviation σ. If X is transformed to Y = 2X + 3, what are the mean and standard deviation of Y?Suppose that Y has an exponential distribution with mean Beta. Show that 2Y/Beta has a chi square distribution with 2 degrees of freedom.
- Find E(X^2) when random variable X has normal distribution with mean(µ) = 7 and standard deviation(σ) = 4.A snack food manufacturer estimates that the variance of the number of grams of carbohydrates in servings of its tortilla chips is 1.23. A dietician is asked to test this claim and finds that a random sample of 24 servings has a variance of 1.27. At α=0.10, is there enough evidence to reject the manufacturer's claim? Assume the population is normally distributed. (b) Find the critical value(s). I do not know how to calculate the critical value with my calculator. I have a TI83+.Suppose a continuous random variable X pdf constant from 0 to 7.516, where the pdf is zero elsewhere. what is variance of this random variable?
