Show that the bias of 0 for estimating 0 is Bias(0) 1 n+1 -0.
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![Let X1,..., Xn be a random sample from a uniform distribution on the interval [20, 0], where
0 < 0. The pdf of X1 is given by
1
20
{
if 20 < x < 0,
f(x|0) =
if x < 20 or x > 0.
Let X(1) < X(2) <...< X(n) be the order statistics of X1, ..., Xn.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F07ef4816-ad15-45ce-8807-966dc9f6e7f3%2Ff40e3bfd-34bd-4b6c-bb62-d53b72ab16b9%2Fjyb9jpsj_processed.png&w=3840&q=75)
Result
Bias(θ)=E(θ^)-θ≠0
Step by step
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- 5) Let Y be binomial (n = 4, II = .3) (a) Calculate the mean and variance by filling in the following table: f(yi) Xi X f(Yi) Yi2 X f(yi) b) Calculate the mean and variance of Y using formulas.Assume that the entire sample has 2 positive observations and 6 negatives observations. Variable X1: at the left branch has 2 positive observations and 4 negatives observations;at the right branch has 6 positive observations and 6 negatives observations. What is the information gain or reduction in uncertainty of X1 using the Gini index? (round to two decimal spaces)For a highway, the car's speed has a uniform distribution [50,90]. Cars are stopped if speed X is greater than 70(mph). The price of a speeding ticket is equal to Y = 15 + (1/10)X(X-70). What is the probability that a stopped car is/was going faster than 85 mph? For each car stopped, the Var(X) is equal to what?
