Let X denote the amount of time a book on two-hour reserve is actually checked out, and suppose the cdf is the following. 0 x < 0 x² F(x) = 0≤x≤ 4 16 1 4 ≤ x Use the cdf to obtain the following. (If necessary, round your answer to four decimal places.) (a) Calculate P(X ≤ 3). (b) Calculate P(2.5 ≤ x ≤ 3). (c) Calculate P(X> 3.5).
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- For T:P5P3 and nullity(T)=4, find rank(T).For T:P4R5, and rank (T)=3, find nullity (T).An instructor has given a short quiz consisting of nvo parts. For a randomly selected student, let X= the number of points earned on the first part and Y= the number of points earned on the second part. Suppose that thejoint pmf of X and Yis given in the accompanying table. a. If the score recorded in the grade book is the total number of points earned on the nvo parts,what isthe expected recorded score E(X + Y)? b. If the maximum of the two scores is recorded,what isthe expected recorded score? A random variable is normally distributed with a mean of m =50 and a standard deviation of <T =5. Sketch a normal curve for the probability density Label the horizontal ax. is with values of 35, 40, 45, 50, 55, 60, and 65. Figure 6.4 shows that the normal curve almost touches the horizontal axis at three standard deviations below and at three standard deviations above the mean (in this case at 35 and 65). What is the probability…
- What degrees of freedom would younormally expect a t test to have when N1 = 40 and N2 = 55?Suppose that a manufacturer is testing one of its machines to make sure that the machine is producing more than 97% good parts (H0: p = 0.97 and Ha : p > 0.97).The test results in a P-value of 0.012. In reality, the machine is producing 97% good parts.What probably happens as a result of our testing? A. We correctly reject H0. B. We fail to reject H0, making a Type II error. C. We reject H0, making a Type I error. D. We fail to reject H0, making a Type I error. E. We correctly fail to reject H0.Persons having Raynaud's syndrome are apt to suffer a sudden impairment of blood circulation in fingers and toes. In an experiment to study the extent of this impairment, each subject immersed a forefinger in water and the resulting heat output (cal/cm2/min) was measured. For m = 9 subjects with the syndrome, the average heat output was x = 0.61, and for n = 9 nonsufferers, the average output was 2.09. Let ?1 and ?2 denote the true average heat outputs for the sufferers and nonsufferers, respectively. Assume that the two distributions of heat output are normal with ?1 = 0.3 and ?2 = 0.5. (a) Consider testing H0: ?1 − ?2 = −1.0 versus Ha: ?1 − ?2 < −1.0 at level 0.01. Describe in words what Ha says, and then carry out the test. Ha says that the average heat output for sufferers is the same as that of non-sufferers.Ha says that the average heat output for sufferers is less than 1 cal/cm2/min below that of non-sufferers. Ha says that the average heat output for sufferers is more…
- LetX1,...,XnbeindependentandidenticallydistributedrandomvariableswithVar(X1)<∞.Showthat1n(n+1)nj=1jXj→pEX1.Suppose that a manufacturer is testing one of its machines to make sure that the machine is producing more than 97% good parts (H0: p = 0.97 and Ha : p > 0.97).The test results in a P-value of 0.102. In reality, the machine is producing 99% good parts.What probably happens as a result of our testing? We correctly fail to reject H0.We reject H0, making a Type I error. We correctly reject H0.We fail to reject H0, making a Type I error.We fail to reject H0, making a Type II error.A random sample of 80 poultry farms of one variety gave an average production of 240 eggs per bird. Another random sample of 50 poultry farms of another variety gave an average production of 195 eggs per bird. At a=0.05 is there sufficient evidence to support that there is a significant difference between the egg production of the two varieties of birds. Assume o1 =18 eggs and o2=15 eggs
- Persons having Raynaud's syndrome are apt to suffer a sudden impairment of blood circulation in fingers and toes. In an experiment to study the extent of this impairment, each subject immersed a forefinger in water and the resulting heat output (cal/cm2/min) was measured. For m = 9 subjects with the syndrome, the average heat output was x = 0.65, and for n = 9 nonsufferers, the average output was 2.03. Let μ1 and μ2 denote the true average heat outputs for the sufferers and nonsufferers, respectively. Assume that the two distributions of heat output are normal witSuppose that a manufacturer is testing one of its machines to make sure that the machine is producing more than 97% good parts (H0: p = 0.97 and Ha : p > 0.97). The test results in a P-value of 0.012. In reality, the machine is producing 97% good parts. What probably happens as a result of our testing? We fail to reject H0, making a Type II error. We reject H0, making a Type I error. We correctly reject H0. We fail to reject H0, making a Type I error. We correctly fail to reject H0.(d) Compute V(X) (in GB2) using the shortcut formula. (Enter your answer to four decimal places.)
