Assume Y1, Y2, . . . , Yn are i.i.d. Normal (μ, σ2) where σ2 is...

Assume Y1, Y2, . . . , Yn are i.i.d. Normal (μ, σ2) where σ2 is known and fixed and the unknown mean μ has a Normal (0,σ2/m) prior, where m is a given constant. Give a 95% credible interval for μ.

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orchestra answered 1 year ago

If you conduct and experiment 1500 times independently, i=1,2,3,...1500. Let y1, y2.... yN be i.i.d observations...

If you conduct and experiment 1500 times independently, i=1,2,3,...1500. Let y1, y2.... yN be i.i.d observations from this experiment, yi=1 if heads with a probability of β; yi=0 if tails with a probability of 1-β. If you get 600 heads and 900 tails, what is the βMLE？ A. 0.4 B. 0.5 C. 0.6 D. 0.7

Consider a random sample (X1, Y1), (X2, Y2), . . . , (Xn, Yn) where Y...

Consider a random sample (X1, Y1), (X2, Y2), . . . , (Xn, Yn) where Y | X = x is modeled by Y=β0+β1x+ε, ε∼N(0,σ^2), where β0,β1and σ^2 are unknown. Let β1 denote the mle of β1. Derive V(βhat1).

(a) Suppose X1, ..., Xn1 i.i.d. ∼ N(µ1, σ2 1 ) and Y1, ...Yn2 i.i.d. ∼...

(a) Suppose X1, ..., Xn1 i.i.d. ∼ N(µ1, σ2 1 ) and Y1, ...Yn2 i.i.d. ∼ N(µ2, σ2 2 ) are independent Normal samples. Suggest an unbiased estimator for µ1 − µ2 and find its’ standard error. Now Suppose n1 = 100, n2 = 200, it is known that σ 2 1 = σ 2 2 = 1, and we calculate X¯ = 5.7, Y¯ = 5.2. Find a 2-standard-error bound on the error of estimation. (b) Suppose X ∼...

5. Let Y1, Y2, ...Yn i.i.d. ∼ f(y; α) = 1/6( α^8 y^3) · e ^(−α...

5. Let Y1, Y2, ...Yn i.i.d. ∼ f(y; α) = 1/6( α^8 y^3) · e ^(−α 2y) , 0 ≤ y < ∞, 0 < α < ∞. (a) (8 points) Find an expression for the Method of Moments estimator of α, ˜α. Show all work. (b) (8 points) Find an expression for the Maximum Likelihood estimator for α, ˆα. Show all work.

Let Y1, Y2, . . ., Yn be a random sample from a uniform distribution on...

Let Y1, Y2, . . ., Yn be a random sample from a uniform distribution on the interval (θ - 2, θ). a) Show that Ȳ is a biased estimator of θ. Calculate the bias. b) Calculate MSE( Ȳ). c) Find an unbiased estimator of θ. d) What is the mean square error of your unbiased estimator? e) Is your unbiased estimator a consistent estimator of θ?

Suppose that X1, X2, , Xm and Y1, Y2, , Yn are independent random samples, with...

Suppose that X1, X2, , Xm and Y1, Y2, , Yn are independent random samples, with the variables Xi normally distributed with mean μ1 and variance σ12 and the variables Yi normally distributed with mean μ2 and variance σ22. The difference between the sample means, X − Y, is then a linear combination of m + n normally distributed random variables and, by this theorem, is itself normally distributed. (a) Find E(X − Y). (b) Find V(X − Y). (c)...

Let Y1, ... , Yn be a random sample that follows normal distribution N(μ,2σ^2) i)get the...

Let Y1, ... , Yn be a random sample that follows normal distribution N(μ,2σ^2) i)get the mle for σ^2 ii)prove using i) that it is an efficient estimator

Let Y1, Y2, ..., Yn be a random sample from an exponential distribution with mean theta....

Let Y1, Y2, ..., Yn be a random sample from an exponential distribution with mean theta. We would like to test H0: theta = 3 against Ha: theta = 5 based on this random sample. (a) Find the form of the most powerful rejection region. (b) Suppose n = 12. Find the MP rejection region of level 0.1. (c) Is the rejection region in (b) the uniformly most powerful rejection region of level 0.1 for testing H0: theta = 3...

y1 = -109.7ln(x)+336.56 y2 = -126.9ln(x)+395.81 where y1 = storage time in days for sprouting y2...

y1 = -109.7ln(x)+336.56 y2 = -126.9ln(x)+395.81 where y1 = storage time in days for sprouting y2 = storage time in days for spoilage x = storage temperature in oC a. How many days are potatoes expected to spoil if stored at 18oC? b. A farmer discovered his stored potatoes showing a sign of wrinkles and dark spot after 15 days. Determine at what temperatures they must has been stored to cause the spoilage. c. A food processing company wants to...

Let Y1 and Y2 have joint pdf f(y1, y2) = (6(1−y2), if 0≤y1≤y2≤1 0, otherwise. a)...

Let Y1 and Y2 have joint pdf f(y1, y2) = (6(1−y2), if 0≤y1≤y2≤1 0, otherwise. a) Are Y1 and Y2 independent? Why? b) Find Cov(Y1, Y2). c) Find V(Y1−Y2). d) Find Var(Y1|Y2=y2).

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