Suppose we collect n samplesX1,X2, . . . ,Xn from a uniform distribution U[θ,1]. We know the maximum likelihood estimator of θ is θ = min(Xi). (1) What is the CDF of θ? (2) What is the pdf of θ? (3) Find the bias of θ. (4) Find the variance of θ. (5) Find the MSE of θ.

T/F question the MSE(theta) for an unbiased estimator is given by its variance.

Suppose you have a joint distribution of x and y where • x has population mean ug and population variance o? • y has population mean ly and population variance o, and the population covariance between them is Ery. The population Pearson correlation is then given by Ery OxJy We collect n pairs of data, (X;, Yi), i = 1,.. , n. Each pair is an independent draw from this distribution. (a) Suppose we estimate our population covariance with n 1 (x; – Ha)(yi – µy). i=1 Is this an unbiased estimator of the population covariance? Show why or why not. (b) Suppose we estimate our correlation with (xi – Ha)(Yi – Hy) - n i=1 Ox0y Is this an unbiased estimator of the population correlation? Show why or why not. =WI

N(0, o?) is For the simple linear model Y = a + BX + €, where the error variable e ~ independent of X, use the law of total variance to show that Var(Y) = 3² Var(X)+o².

Q. Let the joint pmf of x and y be defined by f (x,y) = (x+y)/32  where x = 1,2 and y = 1,2,3,4

What is the covariance for the joint distribution below right? Cov(X, Y) = -1 YO +1 -1 1/16 3/16 1/16 X 0 3/16 0 3/16 +1 1/16 3/16 1/16

Y has a distribution function (0, ys0, 24 F(y) = 0

please teach this

A function has a graph which passes through the point (2,3) and its graph also has the property that the normal line to each point (x,y) on the graph passes through the point (2,0). Find the function?

Plz fast plzzzzzz..asap i'll rate plz fast hand written plz