The lifetime X in hours of a certain electrical component has the pdf
If a random sample of 36 is taken from these components,
find P(3 + 100 < 111)
Here X has exponential distribution with parameter 1/3 So
Since sample size n=36 is greater than 30 so according to CLT sampling distribution of sample mean will be approximately normal with mean and SD as follows:
Now,
The z-score for is
Therefore required probability is
Answer: 0.9082
The lifetime X in hours of a certain electrical component has the pdf If a random...
2. A certain type of electronic component has a lifetime X (in hours) with probability density function given by otherwise. where θ 0. Let X1, . . . , Xn denote a simple random sample of n such electrical components. . Find an expression for the MLE of θ as a function of X1 Denote this MLE by θ ·Determine the expected value and variance of θ. » What is the MLE for the variance of X? Show that θ...
Let X1, X2, ..., Xn be a random sample from X which has pdf depending on a parameter and (i) (ii) where < x < . In both these two cases a) write down the log-likelihood function and find a 1-dimensional sufficient statistic for b) find the score function and the maximum likelihood estimator of c) find the observed information and evaluate the Fisher information at = 1. f(20) We were unable to transcribe this image((z(0 – 2) - )dxəz(47)...
Continuous random variable X has pdf for , where is symmetric about x = 0. Evaluate where is the cumulative distribution function of X and k > 0. fr) We were unable to transcribe this imagefr) We were unable to transcribe this imageFr(r
An electrical firm manufactures a certain type of LED light bulb and claims that the average bulb lifetime is at least 800 hours. To test this, a random sample of 60 bulbs is taken. The average life of the sample is found to be 788 hours with a standard deviation of 40 hours.(a) At a level of 0.05 significance, is there compelling evidence to doubt the comp any's claim? Be sure to state the appropriate hypotheses, and specify the rejection...
What are (a) the x component, (b) the y component, and (c) the z component of if , , and . (d) Calculate the angle between and the positive z axis. (e) What is the component of along the direction of ? (f) What is the magnitude of the component of perpendicular to the direction of but in the plane of and ? We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe...
Let X1,...,X10 be a random sample from N(θ1,1) distribution and let Y1,...,Y10 be an independent random sample from N(θ2,1) distribution. Let φ(X,Y ) = 1 if X < Y , −5 if X ≥ Y , and V= φ(Xi,Yj) . 1. Find v so that P[V>=v]=0.45 when 1=2. 2. Find the mean and variance of V when 1=2. 10 10 2 We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe...
Let be a sample (size n=1) from the exponential distribution, which has the pdf , where is an unknown parameter. Let's define a statistic as . Is a sufficient statistic for ? We were unable to transcribe this imagef(x: λ) = Xe We were unable to transcribe this imageT(X) = 1122 T(X) We were unable to transcribe this image
Suppose that Z is a continuous random variable. Let denote the unnormalized PDF of Z ―the function satisfies all properties of a PDF except that it is not normalized. Now suppose we use to compute something like the moment generating function (MGF), i.e., we compute the function What is ? How can we use to normalize the PDF? b(2) We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable...
Given the pdf Take a sample of size 3 from this pdf. Use the statistic ymax to test H0 : = 5 versus HA : > 5. (a) Find the critical value to give a test of significance = 0.05. (b) Suppose = 7. What is the Type II error for the test in part (a). Θ2 We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe...
Problem 9.5. Suppose that an electrical component manufactured by Johnny Depp Electrical Company is designed to provide a mean service life of 1,000 hours, with a standard deviation of 100 hours. Assume that the service life is normally distributed. (a) When a customer purchases one component, what is the probability that the service life of the component will exceed 1,100 hours? P[ X > 1,100 ] = P[ Z > 1 ] = 15.87% (b) Suppose that a customer purchases...