Let X1. Xn n independent and identically distributed random variables with common mean u=1 and standard deviation o=2. We let X denote the empirical mean of the sample X1., Xn. v Veuillez choisir au moins une réponse : O a. By the law of large number, X"2 when n- O b. By the law of large number, X1 when n Oc. By the central limit theorem, XN(0,1) O d. By the central limit theorem, X-12/n N(0.1) O e. By the central limit theorem, XN(1,2/n). Of. By the central limit theorem, for any a,b whatever the distribution of X1. Xn, P(as X-12/n sb) P(asZsb) where Z-N(0,1).

A. Classify each random variable as discrete or continuous. 1. X: Number of women among 20 newly hired teachers 2. Y: Height (in centimeters) of a 30 randomly selected adult males 3. Z: Number of car accidents among 8 selected cities 4. A: Amount of rainfall (in millimeters) in different cities in Metro Manila 5. B: Number of gifts received by 20 students during Christmas season

Let x be a random variable that represents hemoglobin count (HC) in grams per 100 milliliters of whole blood. Then x has a distribution that is approximately normal, with population mean of about 14 for adult healthy women. Suspose that a female patient  has taken 10 labrotory blood test during the past year. The HC data sent to the patients doctors are as follows:  15  18  16 19  13  13  15  17  17  10 A) x-bar =     s        = B) Does this information indicate that the population average HC for this patient is higher than 14? use alpha= 0.01 what is the level of significance? What is the value of the sample test statistic? Round to 3 decimal places estimate the P-value

Suppose that X has a Weibull distribution with β = 2 and δ = 2400. Determine the following. a. P(X > 5000) = b. For an exponential random variable with the same mean as the Weibull distribution  P(X > 5000) =