Problem 4. Let X1, X2, X3 be a random sample of size n = 3 from a normally distributed random variable with mean 2, variance 12. Let Y = X1 -2X2 + 3X3. (a) Find the mean and the variance of Y. (b) Find P(1 < Y < 5). A ssume that a guantity is normally distributod wrih

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Suppose that we have disjoint normal populations A and B with equal population variances.   Suppose we plan a sample of size 4 from from population A and a sample of size 9 from population B which we will pool to form the pooled variance.  If you know the population variances are both in fact equal to 6, what is the probability that the pooled variance of the two samples will turn out to be less than 8 given your information?

An urn contains 7 black and 18 white balls. A ball is randomly drawn from the urn. Let X = 1 if a white ball is drawn and let X = -1 if a black ball is drawn. Find the following a) mean of X b) variance of X Please provide your working and round your answers to 2 decimal places