Let X1, X2 ,, X8 be a random sample of size 8 from a POI(λ) distribution....
Let X1, X2 ,, X8 be a random sample of size 8 from a POI(λ) distribution. The null hypothesis that λ = 0.25 will be rejected in favor of the alternative hypothesis that λ>0.25 if ∑X ≥5. i
a. Find the probability of committing a type I error. (Hint: If Xi ~ POI(λ), then ∑Xi ~ POI(nλ)).
b. Find the probability of committing a type II error if λ = 0.5 .
c. Find the power of the test if λ=0.5.
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Let X1, X2 ,, X8 be a random sample of size 8 from a POI(λ)
distribution....
Please answer this question using R 20. Let X1, X2, ..., X12 be a random sample...
Please answer this question using R
20. Let X1, X2, ..., X12 be a random sample from a Bernoulli distribution with unknown success probability p. We will test Ho: p = 0.3 versus Ha: p < 0.3, rejecting the null if the number of successes, Y = Dizi Xi, is 0 or 1. (a) Find the probability of a Type I error. (b) If the alternative is true, find an expression for the power, 1 – B, as a function...
6. Let Xi, X2, .., X6 be a random sample from a distribution with density function...
6. Let Xi, X2, .., X6 be a random sample from a distribution with density function 820-1 for 0 < x 1 where θ > 0 f(x; 6) 0 otherwise The null hypothesis Ho : θ-1 is to be rejected in favor of the alternative Ha : θ 1 if and only if at least 5 of the sample observations are larger than 0.7. What is the significance level of the test
Let X1, X2,.......Xn be a random sample of size n from a continuous distribution symmetric about...
Let X1, X2,.......Xn be a
random sample of size n from a continuous distribution symmetric
about .
For testing H0: =
10 vs H1: <
10, consider the statistic T- =
Ri+ (1-i),
where i
=1 if Xi>10 , 0 otherwise; and
Ri+ is the rank of (Xi - 10) among
|X1 -10|, |X2-10|......|Xn
-10|.
1. Find the null mean and variance of T- .
2. Find the exact null distribution of T- for
n=5.
We were unable to transcribe this imageWe were...
Let X1, X2,.,X10 be a sample of size 10 from an exponential distribution with the density function Sae -Xx f(x; A) othe...
Let X1, X2,.,X10 be a sample of size 10 from an exponential distribution with the density function Sae -Xx f(x; A) otherwise 10 We reject Ho : ^ = 1 in favor of H : 1 = 2 if the observed value of Y = smaller than 6 (a) Find the probability of type 1 error for this test. (b) Find the probability of type 2 error for this test (c) Let y5 be the observed value of Y. Find...
2. Let X1,.n be a random sample from the density 0 otherwise Suppose n = 2m+...
2. Let X1,.n be a random sample from the density 0 otherwise Suppose n = 2m+ 1 for some integer m. Let Y be the sample median and Z = max(Xi) be the sample maximum (a) Apply the usual formula for the density of an order statistic to show the density of Y is (b) Note that a beta random variable X has density f(x) = TaT(可 with mean μ = α/(a + β) and variance σ2 = αβ/((a +s+...
Let X1, X2,... X,n be a random sample of size n from a distribution with probability...
Let X1, X2,... X,n be a random sample of size n from a distribution with probability density function obtain the maximum likelihood estimator of λ, λ. Calculate an estimate using this maximum likelihood estimator when 1 0.10, r2 0.20, 0.30, x 0.70.
suppose X1, X2 is a random sample of size n = 2 from a population distribution....
suppose X1, X2 is a random sample of size n = 2 from a
population distribution.
i) compute P(X1=X2)
ii) what is the probability that the sample mean is less than
1.5?
T 0 1 2 P(x) 0.2 0.5 0.3
1. Let X1, X2,... .Xn be a random sample of size n from a Bernoulli distribution...
1. Let X1, X2,... .Xn be a random sample of size n from a Bernoulli distribution for which p is the probability of success. We know the maximum likelihood estimator for p is p = 1 Σ_i Xi. ·Show that p is an unbiased estimator of p.
Let X1, X2, ..., X8 be a random sample of size n=8 from a normally-distributed population...
Let X1, X2, ..., X8 be a random sample of size n=8 from a normally-distributed population whose mean is 7.9 and variance is 1.1. What are the mean and variance of the sample mean X? E[X] - 7.9, Var(X) 0.138 E[X] =0.988, Var(X) = 0.138 E[X] = 7.9, Var(8) = 1.1 E[X] =0.988, Var(87) - 1.1
1(a) Let Xi, X2, the random interval (ay,, b%) around 9, where Y, = max(Xi,X2 ,X),...
1(a) Let Xi, X2, the random interval (ay,, b%) around 9, where Y, = max(Xi,X2 ,X), a and b are constants such that 1 S a <b. Find the confidence level of this interval. Xi, X, want to test H0: θ-ya versus H1: θ> %. Suppose we set our decision rule as reject Ho , X, be a random sample from the Uniform (0, θ) distribution. Consider (b) ,X5 is a random sample from the Bernoulli (0) distribution, 0 <...
Please answer this question using R
20. Let X1, X2, ..., X12 be a random sample from a Bernoulli distribution with unknown success probability p. We will test Ho: p = 0.3 versus Ha: p < 0.3, rejecting the null if the number of successes, Y = Dizi Xi, is 0 or 1. (a) Find the probability of a Type I error. (b) If the alternative is true, find an expression for the power, 1 – B, as a function...
6. Let Xi, X2, .., X6 be a random sample from a distribution with density function 820-1 for 0 < x 1 where θ > 0 f(x; 6) 0 otherwise The null hypothesis Ho : θ-1 is to be rejected in favor of the alternative Ha : θ 1 if and only if at least 5 of the sample observations are larger than 0.7. What is the significance level of the test
Let X1, X2,.......Xn be a
random sample of size n from a continuous distribution symmetric
about .
For testing H0: =
10 vs H1: <
10, consider the statistic T- =
Ri+ (1-i),
where i
=1 if Xi>10 , 0 otherwise; and
Ri+ is the rank of (Xi - 10) among
|X1 -10|, |X2-10|......|Xn
-10|.
1. Find the null mean and variance of T- .
2. Find the exact null distribution of T- for
n=5.
We were unable to transcribe this imageWe were...
Let X1, X2,.,X10 be a sample of size 10 from an exponential distribution with the density function Sae -Xx f(x; A) otherwise 10 We reject Ho : ^ = 1 in favor of H : 1 = 2 if the observed value of Y = smaller than 6 (a) Find the probability of type 1 error for this test. (b) Find the probability of type 2 error for this test (c) Let y5 be the observed value of Y. Find...
2. Let X1,.n be a random sample from the density 0 otherwise Suppose n = 2m+ 1 for some integer m. Let Y be the sample median and Z = max(Xi) be the sample maximum (a) Apply the usual formula for the density of an order statistic to show the density of Y is (b) Note that a beta random variable X has density f(x) = TaT(可 with mean μ = α/(a + β) and variance σ2 = αβ/((a +s+...
Let X1, X2,... X,n be a random sample of size n from a distribution with probability density function obtain the maximum likelihood estimator of λ, λ. Calculate an estimate using this maximum likelihood estimator when 1 0.10, r2 0.20, 0.30, x 0.70.
suppose X1, X2 is a random sample of size n = 2 from a
population distribution.
i) compute P(X1=X2)
ii) what is the probability that the sample mean is less than
1.5?
T 0 1 2 P(x) 0.2 0.5 0.3
1. Let X1, X2,... .Xn be a random sample of size n from a Bernoulli distribution for which p is the probability of success. We know the maximum likelihood estimator for p is p = 1 Σ_i Xi. ·Show that p is an unbiased estimator of p.
Let X1, X2, ..., X8 be a random sample of size n=8 from a normally-distributed population whose mean is 7.9 and variance is 1.1. What are the mean and variance of the sample mean X? E[X] - 7.9, Var(X) 0.138 E[X] =0.988, Var(X) = 0.138 E[X] = 7.9, Var(8) = 1.1 E[X] =0.988, Var(87) - 1.1
1(a) Let Xi, X2, the random interval (ay,, b%) around 9, where Y, = max(Xi,X2 ,X), a and b are constants such that 1 S a <b. Find the confidence level of this interval. Xi, X, want to test H0: θ-ya versus H1: θ> %. Suppose we set our decision rule as reject Ho , X, be a random sample from the Uniform (0, θ) distribution. Consider (b) ,X5 is a random sample from the Bernoulli (0) distribution, 0 <...
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