Assume X is a Poisson random variable with parameter lambda. What is the test statistic and...

Assume X is a Poisson random variable with parameter lambda. What is the test statistic and the best critical region for testing

H_0:lambda = lambda_0 versus H_a:lambda = lambda_1

where lambda_0 < lambda_1 are constants?

Solutions

Expert Solution

orchestra answered 1 year ago

Next > < Previous

Related Solutions

Suppose X is a Gamma random variable with shape parameter α and scale parameter θ >...

Suppose X is a Gamma random variable with shape parameter α and scale parameter θ > 0, i.e., the pdf is given as, f(x|α, θ) = 1 Γ(α)θ α x α−1 e −x/θ , 0 < x < ∞, (1) where α > 0, θ > 0 and Γ(a) = Z ∞ 0 x a−1 e −x dx. HINT: see section 3.2 of the textbook. (a) What is the support of X? That is, X = ? (b) Show that...

X is a random variable following Poisson distribution. X1 is an observation (random sample point) of...

X is a random variable following Poisson distribution. X1 is an observation (random sample point) of X. (1.1) Please find probability distribution of X and X1. Make sure to define related parameter properly. (1.2) Please give the probability distribution of a random sample with sample size of n that consists of X1, X2, ..., Xn as its observations. (1.3) Please give an approximate distribution of the sample mean in question 1.2(say, called Y) when sample size is 100 with detailed...

A random variable X is said to follow the Weibull distribution with shape parameter

A random variable $X$ is said to follow the Weibull distribution with shape parameter $\alpha$ and scale parameter $\beta$, written $W(\alpha, \beta)$ if its p.d.f. is given by $$ f(x)=\frac{\alpha}{\beta^{\alpha}} x^{\alpha-1} e^{-\left(\frac{g}{3}\right)^{\alpha}} $$ for $x>0$. The Weibull distribution is used to model lifetime of item subject to failure. If $\alpha \in(0,1),$ it is used to model decreasing failure rate overtime, whereas if $\alpha>1,$ one models increasing failure rate over time. It is easy to show that the c.d.f. of $X$...

Let x be an exponential random variable with lambda equals 0.2. Calculate the probabilities described below....

Let x be an exponential random variable with lambda equals 0.2. Calculate the probabilities described below. a. P(x<7) b. P(x>8) c. P(7< = x < = 8) d. P(x> = 6) e. the probability that x is at most 8

The random variable X has an Exponential distribution with parameter beta= 5. The P(X > 18|X...

The random variable X has an Exponential distribution with parameter beta= 5. The P(X > 18|X > 12) is equal to

What is the difference between a statistic and a parameter?

let X~GAM(3,2), when X = x, conditional distribution of Y has parameter as lambda = x,...

let X~GAM(3,2), when X = x, conditional distribution of Y has parameter as lambda = x, ~ POI(lambda) (a) what is E(Y) and Var(Y)? (b) what is marginal distribution of Y? (c) what is E(X|Y=15) and Var(X|Y=15)?

1. If the random variable x has a Poisson Distribution with mean μ = 53.4, find...

1. If the random variable x has a Poisson Distribution with mean μ = 53.4, find the maximum usual value for x. Round your answer to two decimal places. 2. In one town, the number of burglaries in a week has a Poisson distribution with mean μ = 7.2. Let variable x denote the number of burglaries in this town in a randomly selected month. Find the smallest usual value for x. Round your answer to three decimal places. (HINT:...

Let X be an exponential random variable with parameter λ, which means that fX(x) = λe^(−λx)...

Let X be an exponential random variable with parameter λ, which means that fX(x) = λe^(−λx) * u(x). (a) For x > 0, find P(X ≤ x). (b) For x2 > x1 > 0, find P(x1 ≤ X ≤ x2). (c) For x > 0, find P(X ≥ x). (d) Segment the positive real line into three equally likely disjoint intervals.

Assume that the number of defects in a car has a Poisson distribution with parameter 𝜆.

Assume that the number of defects in a car has a Poisson distribution with parameter 𝜆. To estimate 𝜆 we obtain the random sample 𝑋1,𝑋2, … , 𝑋n.a. Find the Fisher information is a single observation using two methods.b. Find the Cramer-Rao lower bound for the variance of an unbiased estimator of 𝜆.c. Find the MLE of 𝜆 and show that the MLE is an efficient estimator.

Subjects