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(a)-(d)? Problem(11) (10 points) Let Z~Normal(0, 1). Recall the definition of -value, i.e., P(Z>)-r. (a) (1...
(b) (c) and (d) please Problem(5) (a) (1 pt) Let Z~ Normal(0, 1). Recall the definition...
(b)
(c) and (d) please
Problem(5) (a) (1 pt) Let Z~ Normal(0, 1). Recall the definition of z-value, i.e., P(Z > zr) = r. Find the probability of P(-70/2 < 3 < 2a/2). (b) (4 points) Let X1, X2, ... , Xn be a random sample from some population with (un- known) mean u and (known) variance o?. Based on the Central Limit Theorem and part (a) above, show that the confidence intervals for the population mean y can be...
Normal (0, 1) Recall the definition of z-value, e. Problem(1) (a) (2 points) Let Z P(Z>2r....
Normal (0, 1) Recall the definition of z-value, e. Problem(1) (a) (2 points) Let Z P(Z>2r. Find the probability of P(-za/2<Z< za/2) .
Normal (0, 1) Recall the definition of z-value, e. Problem(1) (a) (2 points) Let Z P(Z>2r. Find the probability of P(-za/2
show me all work for the problem i,ii,iii Exercise 1 (Sample size for estimating the mean)....
show me all work for the problem i,ii,iii
Exercise 1 (Sample size for estimating the mean). Let X1,...,x, be i.i.d. samples from some un- known distribution of mean u. Let X and S denote the sample mean and sample variance. Fix a E (0,1) and € >0. (i) Suppose the population distribution is N(uo?) for known op > 0. Recall that we have the following 100(1 - a)% confidence interval for : (1) Deduce that plue (x-Zalze in 2+ zarze...
Let X ~ N(0, 1), and let Z ~ Unif{-1, 1} (i.e. P(Z = -1) =...
Let X ~ N(0, 1), and let Z ~ Unif{-1, 1} (i.e. P(Z = -1) = P(Z = 1) = 1/2) be independent of X. Let Y = ZX. What is the distribution of Y? Show that X and Y are uncorrelated. Are X and Y independent?
Problem 1 Let Xi, ,Xn be a random sample from a Normal distribution with mean μ and variance 1.e Answer the following questions for 8 points total (a) Derive the moment generating function of the dis...
Problem 1 Let Xi, ,Xn be a random sample from a Normal distribution with mean μ and variance 1.e Answer the following questions for 8 points total (a) Derive the moment generating function of the distribution. (1 point). Hint: use the fact that PDF of a density always integrates to 1. (b) Show that the mean of the distribution is u (proof needed). (1 point) (c) Using random sample X1, ,Xn to derive the maximum likelihood estimator of μ (2...
by confidence intervals, normal distributed data, known variance Equation 1: If is the sample mean of...
by confidence intervals, normal distributed data, known
variance
Equation 1: If is the sample mean of a random sample of size n from a normal population with known variance o2, a 100 (1- a)% CI on u is given by HIZa/2 n SHST+/2 Vn is the upper 100g percentage point of the standard normal distribution. a/2 where 17. If the sample size n is doubled, by how much is the length of the CI on u in Equation 1 reduced?...
Problem 1. Let X be a normal random variable with mean 0 and variance 1 and...
Problem 1. Let X be a normal random variable with mean 0 and variance 1 and let Y be uniform(0.1) with X and Y being independent. Let U-X + Y and V = X-Y. For this problem recall the density for a normal random variable is 2πσ2 (a) Find the joint distribution of U and V (b) Find the marginal distributions of U and V (c) Find Cov(U, V).
(4 points) Let Xi, , Xn denote a randon sample from a Normal N(μ, 1) distribution, with 11 as the...
please answer with full soultion. with explantion.
(4 points) Let Xi, , Xn denote a randon sample from a Normal N(μ, 1) distribution, with 11 as the unknown parameter. Let X denote the sample mean. (Note that the mean and the variance of a normal N(μ, σ2) distribution is μ and σ2, respectively.) Is X2 an unbiased estimator for 112? Explain your answer. (Hint: Recall the fornula E(X2) (E(X)Var(X) and apply this formula for X - be careful on the...
11. Do one of the following, as appropriate: (a) Find the critical value z a, (b)...
11. Do one of the following, as appropriate: (a) Find the critical value z a, (b) find the critical value (ipoint tap, (c) state that neither the normal nor the t distribution applies. 99%; n = 17, σ is unknown; population appears to be normally distributed. O zan 2.583 O tan a/2 -2.898 O ta/2-2921 O za/2#2567 12. Do one of the following, as appropriate: (a) Find the critical value za/2, (b) find the critical value (point) tan,(c) state that...
Problem 8. (15 points) Let x be a random variable that represents the hemoglobin count (HC)...
Problem 8. (15 points) Let x be a random variable that represents the hemoglobin count (HC) in human blood (measured in grams per milliliter). In healthy adult females, x has an approximately normal distribution with a population mean of u = 14.2, and population standard deviation of o = 2.5. Suppose a female patient had 10 blood tests over the past year, and the sample mean HC was determined to be x = 15.1. a. What is the value of...
(b)
(c) and (d) please
Problem(5) (a) (1 pt) Let Z~ Normal(0, 1). Recall the definition of z-value, i.e., P(Z > zr) = r. Find the probability of P(-70/2 < 3 < 2a/2). (b) (4 points) Let X1, X2, ... , Xn be a random sample from some population with (un- known) mean u and (known) variance o?. Based on the Central Limit Theorem and part (a) above, show that the confidence intervals for the population mean y can be...
Normal (0, 1) Recall the definition of z-value, e. Problem(1) (a) (2 points) Let Z P(Z>2r. Find the probability of P(-za/2<Z< za/2) .
Normal (0, 1) Recall the definition of z-value, e. Problem(1) (a) (2 points) Let Z P(Z>2r. Find the probability of P(-za/2
show me all work for the problem i,ii,iii
Exercise 1 (Sample size for estimating the mean). Let X1,...,x, be i.i.d. samples from some un- known distribution of mean u. Let X and S denote the sample mean and sample variance. Fix a E (0,1) and € >0. (i) Suppose the population distribution is N(uo?) for known op > 0. Recall that we have the following 100(1 - a)% confidence interval for : (1) Deduce that plue (x-Zalze in 2+ zarze...
Let X ~ N(0, 1), and let Z ~ Unif{-1, 1} (i.e. P(Z = -1) = P(Z = 1) = 1/2) be independent of X. Let Y = ZX. What is the distribution of Y? Show that X and Y are uncorrelated. Are X and Y independent?
Problem 1 Let Xi, ,Xn be a random sample from a Normal distribution with mean μ and variance 1.e Answer the following questions for 8 points total (a) Derive the moment generating function of the distribution. (1 point). Hint: use the fact that PDF of a density always integrates to 1. (b) Show that the mean of the distribution is u (proof needed). (1 point) (c) Using random sample X1, ,Xn to derive the maximum likelihood estimator of μ (2...
by confidence intervals, normal distributed data, known
variance
Equation 1: If is the sample mean of a random sample of size n from a normal population with known variance o2, a 100 (1- a)% CI on u is given by HIZa/2 n SHST+/2 Vn is the upper 100g percentage point of the standard normal distribution. a/2 where 17. If the sample size n is doubled, by how much is the length of the CI on u in Equation 1 reduced?...
Problem 1. Let X be a normal random variable with mean 0 and variance 1 and let Y be uniform(0.1) with X and Y being independent. Let U-X + Y and V = X-Y. For this problem recall the density for a normal random variable is 2πσ2 (a) Find the joint distribution of U and V (b) Find the marginal distributions of U and V (c) Find Cov(U, V).
please answer with full soultion. with explantion.
(4 points) Let Xi, , Xn denote a randon sample from a Normal N(μ, 1) distribution, with 11 as the unknown parameter. Let X denote the sample mean. (Note that the mean and the variance of a normal N(μ, σ2) distribution is μ and σ2, respectively.) Is X2 an unbiased estimator for 112? Explain your answer. (Hint: Recall the fornula E(X2) (E(X)Var(X) and apply this formula for X - be careful on the...
11. Do one of the following, as appropriate: (a) Find the critical value z a, (b) find the critical value (ipoint tap, (c) state that neither the normal nor the t distribution applies. 99%; n = 17, σ is unknown; population appears to be normally distributed. O zan 2.583 O tan a/2 -2.898 O ta/2-2921 O za/2#2567 12. Do one of the following, as appropriate: (a) Find the critical value za/2, (b) find the critical value (point) tan,(c) state that...
Problem 8. (15 points) Let x be a random variable that represents the hemoglobin count (HC) in human blood (measured in grams per milliliter). In healthy adult females, x has an approximately normal distribution with a population mean of u = 14.2, and population standard deviation of o = 2.5. Suppose a female patient had 10 blood tests over the past year, and the sample mean HC was determined to be x = 15.1. a. What is the value of...
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