(20 points) Suppose X~N(25, 81). That is, X has a normal distribution with μ-25 and σ-81...
(20 points) Suppose X-N(25, 81). That is, has a normal distribution with μ-25 and σ2-81. la. Find a transformation of X that will give it a mean of zero and a variance of one (ie., standardize X). lb. Find the probability that 18<x < 26. 1c. Supposing Y = 10 +5X, find the mean of Y 1d. Find the variance of Y
Let the random variable X follow a normal distribution with μ =40 and σ^2 =81. The probability is 0.03 that X is in the symmetric interval about the mean between which two numbers? Round to one decimal place as needed. Use ascending order
Suppose x has a distribution with μ = 35 and σ = 18. (a) If random samples of size n = 16 are selected, can we say anything about the x distribution of sample means? Yes, the x distribution is normal with mean μ x = 35 and σ x = 4.5. No, the sample size is too small. Yes, the x distribution is normal with mean μ x = 35 and σ x = 18. Yes, the x distribution...
Suppose x has a distribution with μ = 32 and σ = 17. (a) If random samples of size n = 16 are selected, can we say anything about the x distribution of sample means? No, the sample size is too small. Yes, the x distribution is normal with mean μ x = 32 and σ x = 17. Yes, the x distribution is normal with mean μ x = 32 and σ x = 1.1. Yes, the x distribution...
Problem3 (15 points (a) (8 points) Let x, X, be a random sample from normal distribution NG, σ, . s are sample mean and sample variance. Consider the probabilities PC, μ) and PS? σ)-are they equal? (b) (7 points) Let X, , ,X, be a random sample from normal distribution Mo, σ, R, s are sample mean and sample variance. Let y.... is and independent sample from the same distribution. Y, s are corresponding sample mean and sample variance. Let...
Let X have a normal distribution with mean μ and variance σ ^2 . The highest value of the pdf is equal to 0.1 and when the value of X is equal to 10, the pdf is equal to 0.05. What are the values of μ and σ?
A population of values has a normal distribution with μ=81μ=81 and σ=39σ=39. You intend to draw a random sample of size n=176n=176. State answers to one decimal places. Find P92, which is the score separating the bottom 92% scores from the top 8% scores. P92 (for single values) = Find P92, which is the mean separating the bottom 92% means from the top 8% means. P92 (for sample means) =
Given a normal distribution with μ = 27 and σ = 25. If a random sample of size n = 72 is drawn, find P(27 ≤ x ≤ 29). Round to three decimal places.
DISTRIBUTION OF SAMPLE VARIANCE:
Xn ~ N(μ, σ2), where both μ and σ are Problem 4 (25 points). Assume that Xi unknowin 1. Using the exact distribution of the sample variance (Topic 1), find the form of a (1-0) confidence interval for σ2 in terms of quantiles of a chi-square distribution. Note that this interval should not be symmetric about a point estimate of σ2. [10 points] 2. Use the above result to derive a rejection region for a level-o...
8) Let Yi, X, denote a random sample from a normal distribution with mean μ and variance σ , with known μ and unknown σ' . You are given that Σ(X-μ)2 is sufficient for σ a) Find El Σ(X-μ). |. Show all steps. Use the fact that: Var(Y)-E(P)-(BY)' i-1 b) Find the MVUE of σ.