We have N i.i.d random variables from the uniform distribution between 0 and 1. If N=1, what is the probability that the nth order statistic is less than or equal to the value x? (In other words, what is Pr(X(n)1≤x)?)
You say that there are N iid random variables and next N=1.
Hence there is only one random variable
So nth order statistics is same as the original random variable.
So P(X(n)<=x) = P(X<=x)=x, 0<x<1
We have N i.i.d random variables from the uniform distribution between 0 and 1. If N=1,...
5. Let X1, X2,... , X100 be i.i.d. random variables, following the normal distribution N(0, 102). Let α denote the probability that there are at least 3 variables among them whose absolute value is larger than 19.6. Compute α, and give an approxi- mate value of α with an error less than 0.01 according to the Poisson distribution. 15pts] 5. Let X1, X2,... , X100 be i.i.d. random variables, following the normal distribution N(0, 102). Let α denote the probability...
Suppose that the random variables X,..Xn are i.i.d. random variables, each uniform on the interval [0, 1]. Let Y1 = min(X1, ,X, and Yn = mar(X1,-..,X,H a. Show that Fri (y) = P(Ks y)-1-(1-Fri (y))". b. Show that and Fh(y) = P(, y) = (1-Fy(y))". c. Using the results from (a) and (b) and the fact that Fy (y)-y by property of uniform distribution on [0, 11, find EMI and EIYn]
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1) LetX,, ,X, be i.i.d. Uniform (0 , ) random variables for some > 0 (unknown). Which of the following estimators of0 are unbiased and which ones are biased? For each of the biased estimators ofO, find the MSE. (a)2X, (b) the smallest order statistic, (e) the largest order statistic, (d) x, /2 ) For each of the unbiased estimators of 0 in the above problem, find the variance. Which unbiased estimator has the smallest variance? Find the relative efficiency...
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Suppose Yi, i=1, 2, ,…,n, are i.i.d. random variables, each distributed N(2,25). Compute Pr(0 < < 2) for a sample size of 9. Please answer this question with a graph
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