Consider the discrete random variable XX given in the table below. Calculate the mean, variance, and standard deviation of XX. XX 1 3 13 14 15 18 20 P(XX) 0.14 0.13 0.3 0.11 0.08 0.11 0.13

Find the F-test statistic to test the claim that the variances of the two populations are equal. Both distributions are normal. The populations are independent. The standard deviation of the first sample is 6.5752 7.3865 is the standard deviation of the second sample.

Consider a random sample of size n from a normal distribution with unknown mean u and unknown variance o?. Suppose the sample mean is X and the sample variance is S?. n = 16, the observed sample mean i is 8.9. the observed sample variance s is 25 and µo = 10.5. Suppose we now want to test Ho : o² = of versus H1 : o? + of. Which of these test statistics should we use? Select one: O a. W = (n-1)s O b. Z X-P O c. T = S/n Let of = 36. What is the (appropriate) observed test statistic? Give answer to three decimal places.

Find the variance and standard deviation of the following random variable. Hint: start by writing the distribution for the random variable X2 . x P(X = x) 0 0.5 1 0.2 2 0.3

Consider the discrete random variable X given in the table below. Calculate the mean, variance, and standard deviation of X. X P(X) 0²= J = 1 4 5 12 17 0.14 0.09 0.13 0.57 0.07 What is the expected value of X?

Consider the discrete random variable X given in the table below. Calculate the mean, variance, and standard deviation of X. μl = 0²: 0 = II X P(X) 2 3 6 0.14 0.39 0.1 What is the expected value of X? 10 13 15 18 0.08 0.14 0.08 0.07 (All answers should be rounded to one more decimal place than the raw data.) (Round to one decimal place.)

The lifetime of a certain residential air conditioner is normally distributed with a mean of 20 years and a standard deviation of 2 years. Find the probability that if one of these air conditioners is randomly selected, it will last between 19 years and 19.5 years. DII 00.093 O 0.401 00.309 00.290 O None of these Submit Question 4 R V F4 % 5 T G F5 6 Y H N F6 & 7 J 8 M PrtScn K O Home 9 End 0 F10 P

Find the mean, variance, and standard deviation of the binomial distribution with the given values of n and p. n= 122, p = 0.77 The mean, µ, is (Round to the nearest tenth as needed.) The variance, o2, is (Round to the nearest tenth as needed.) The standard deviation, o, is (Round to the nearest tenth as needed.)