Derive LR and Wald test for exponential distribution.
70.If X has an exponential distribution with parameter ⋋, derive a general expression for the (100p)th percentile of the distribution. Then specialize to obtain the median.
hey I need solution asap
thank you
provide step by step solution please
que 5
(a) Find and-2 logA. (b) Determine the Wald-type test. (c) What is Rao's score statistic? 5. Let Xi, Xz, Determine the likelihood ratio test for Hū: β- xn be a random sample from a ra, β)-distribution where α is known and β > 0. against H1:β
(a) Find and-2 logA. (b) Determine the Wald-type test. (c) What is Rao's score statistic? 5. Let Xi, Xz,...
Q6: Let X1, ..., Xn be a random sample of size n from an exponential distribution, Xi ~ EXP(1,n). A test of Ho : n = no versus Hain > no is desired, based on X1:n. (a) Find a critical region of size a of the form {X1:n > c}. (b) Derive the power function for the test of (a).
I have calculated sensitivity, specificity, PPV, NPV, LR(+), and LR(-) for the test below. My question is how to describe the test, i.e. good/bad, any features to notice? Condition Present Condition Absent Total Test + 83 8 91 Test - 6 22 28 Total 89 30 119 Sensitivity = 0.93 Specificity = 0.73 PPV = 0.91 NPV = 0.79 LR(+) = 3.44 LR(-) = 0.095
Please show as much work, the video really did not help :(
Derive the cumulative distribution function (CDF) for a
exponential distribution
X∼exp(λ)
Calculate
P(X≥3) when λ=2
(Correct answer is ~0.0025)
X ~ exp(A) P(X 2 3) ー2 Watch the following video on the Exponential distribution: Link e Exponential Distribution Ax oAX 11:49 / 22:52 * YouTube 57 Minimize Video Derive the cumulative distribution function (CDF) for a exponential distribution X~ exp(a) Calculate P (X 2 3) when A 2...
X is a Laplace Distribution (Double Exponential Distribution) with mu = beta and b = alpha. f(x) = where alpha > 0 Derive an Expression for E(|X - E(X)|). (The expected value of the absolute value of X - the mean).
Suppose X1,X2, ,Xm are iid exponential with mean A. Suppose Yı,Yo, exponential with mean β2-Suppose the samples are independent. , Yn are iid (a) Derive the likelihood ratio test (LRT) statistic λ(x,y) for testing versus and show that it is a function of ti-ti (x)-Σ-iz; and t2-t2(y)-Σ1Uj. (b) Show how you could perform a size a test in part (a) using the F distribution
Suppose X1,X2, ,Xm are iid exponential with mean A. Suppose Yı,Yo, exponential with mean β2-Suppose the...
Derive the generalized likelihood-ratio test for testing whether the correlation of a bivariate normal distribution is 0.
2. Let Xi, , Х, be a random sample gamma(a, β). In parts (a-(d) assume a is known. 30 points a. Consider testing H. : β--βο. Derive Wald statistic for testing H, using the MLE of B both in the numerator and denominator of the statistic. b. Derive a test statistic for testing H, using the asymptotic distribution of the MLE of β. What is the relation between the two statistics in parts (a) and (b)? c. Derive the Score...
Let X1, , xn be a random sample gamma(a, β). In parts (a)-(d) assume a is known. Consider testing Ho : β Derive Wald statistic for testing Ho using the MLE of β both in the numerator and denominator of the statistic.
Let X1, , xn be a random sample gamma(a, β). In parts (a)-(d) assume a is known. Consider testing Ho : β Derive Wald statistic for testing Ho using the MLE of β both in the numerator and...