Y|0~f(yle) = I(y E {1,...,0}), i.e., the data Y is 0(1+0) 10) that has the unknown parameter 8. The possible valu vhere both values have the same prior probability. Suppe ind the posterior PMF of using a Bayesian update table in your calculations and answers.
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- Suppose that X1, . . . , Xn is a random sample from the Normal distribution N (0, σ2 ) with parameter σ > 0, Find the Maximum Likelihood Estimation of σ.Let y1,y2,...,y10 be a random sample from an exponential pdf with unknown parameter λ. Find the form of the Generalized Likelihood Ratio Test for H0: λ = λ0 versus H1: λ doesn't equal λ0. What integral would have to be evaluated to determine the critical value if α were equal to 0.05?If y1, y2,..., ym be a random sample taken from a normal distribution with parameters x and n× n, then the likelihood equation is
- Suppose that the unknown X is uniformly distributed between 0 and 1. What is the expected value of (X^4+2x+1)?If Y is a continuous, uniformly distributed random variable over the interval(4,10), then the value of the PDF between 4 and 10 is?Let X be a continuous random variable with mean μ and standard deviation σ. If X is transformed to Y = 2X + 3, what are the mean and standard deviation of Y?
- A simple random sample of size n =66, is obtained from a population that is skewed left with =33 and =3. . Does the population need to be normally distributed for the sampling distribution of x to be approximately normally distributed? Why? What is the sampling distribution of x? Does the population need to be normally distributed for the sampling distribution of x to be approximately normally distributed? Why?(A) Yes. The central limit theorem states that the sampling variability of nonnormal populations will increase as the sample size increases. (B) Yes. The central limit theorem states that only for underlying populations that are normal is the shape of the sampling distribution of x normal, regardless of the sample size, n. (C)No. The central limit theorem states that only if the shape of the underlying population is normal or uniform does the sampling distribution of x, become approximately normal as the sample size, n, increases. (D) No. The central limit theorem…What should be the value of a to make this continuous random variable X valid?Consider a continuous random variable X such that P (−1 ≤ X ≤ 1) = 1/2. Can X be characterized by i) Uniform, and ii) Exponential distributions? If yes, find the distribution parameters which ensure the required property for X .
- A manufacturer has developed a new fishing line, which he claims has a mean breaking strength of 15 kilograms with a standard deviation of 0.5 kilogram. To test the hypothesis that μ=15μ=15 kilograms against the alternative that p<15p<15 kilograms, a random sample of 50 lines will be tested. The critical region is defined to be x<14.9x<14.9(a) Find the probability of committing a type 1 error when H0H0 is true(b) Evaluate ββ for the alternatives p−14.8p−14.8 and μ=μ= 14.9 kilograms.If Y1,...,Yn denote a random sample of sizenfrom the normal distribution with known mean μ and variance σ2= 25, find the method of moment estimator of μ.Consider a random sample X1, . . . , Xn of size n ≥ 2 from the normal distribution N (0, σ2 ) with parameter σ2 > 0 Suppose that the prior distribution for σ2 is inverse Gamma with density