Let X1, X2,..., X, be a random sample from f(x; 0) = 0e-0¤ Io,0)(x). Find a 100y or (1 – a)100 percent confidence interval for the mean of the population.
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- Let X and Y be independent random variables, each with mean=mu and variance=sigma^2. Find the expression of the correlation of X and XY in terms of mu and sigma.Let X1,X2,.,X, be a random sample from f(x;8) = 0e-8xIq0,c0) (x). Find a 100y or (1 - a)100 percent confidence interval for the mean of the population.Q3/A/ Let X be a r.v with p.d.f f(x) = e-lkl - oIf independent random variables 'X' and 'Y' have the variances 36 and 16 respectively, find the correlation coefficient between (X + Y) and (X- Y) assuming X and Y are zero mean.Show that the variance of a geometric random variable X; is given by V ar(X) = q/p^2 .Suppose we want to test the hypothesis that mothers with low socioeconomic status (SES) deliver babies whose birth weights are different from normal. To test this hypothesis, a random sample of 100 birth weights is selected from a list of full-term babies of SES mothers. The mean birth weight is found to be 115 oz. Suppose the average birth weight of all babies (based on nationwide surveys of millions of deliveries) is known to be 120 oz with = 24 oz. Set = .05 Assume all conditions are met, what is the p-value of their test? Give your answer to 4 decimal places.The annual rainfall (in inches) in a certain region is normally distributed with meanµ = 40 and variance σ^2 = 25. Find the probability that between 35 and 50 inches of rain will fall in theregion in the year 2021. Express your final answer in terms of the standard normalcumulative distribution function Φ. What is the probability that in at least 2 of the next 10 years less than 20inches of rain are recorded in the region?For each random variable defined, describe the set of possible values for the variable, and state whether the variable is discrete or continuous. (a) U = number of times a surfer has to paddle in front of a wave before catching one (b) X = length of a randomly selected angelfishThe life of an electronic device is known to have the exponential distributionwith parameter lamda=1/1000 .(i) What is the probability that the device lasts more than 1000 hours?(ii) What is the probability it will last less than 1200 hours?(iii) Find the mean and variance of the life of the electronic device.Let a and b be any real numbers and let x = (x1,Xz -- -- Xp m-, X) be a data set with a sample mean f and a sample variance s. Show that if y, = (ax, + b), then S3 = a*s;Assume the sample variances to be continuous measurements, find the probability that a random sample of 25 observations, from a normal population with variance = 6, will have a sample variance s^2 (a) greater than 9.1; (b) between 3.462 and 10.745Let the probability function of the random variable X be defined as f(x)=c/x^4 for x>1, otherwise f(x)=0. Calculate the constant c, the expected value and the variance.SEE MORE QUESTIONS