Complete the given relative frequency distribution. Outcome 1 Rel. Frequency 0.4 Compute the relative frequencies. (a) P({2, 3, 4}) (b) P(E') where E = {3,4} 2 3 0.3 4 0.1 5 0.1

х1 x2 x3 13.92 3.5 94 13.85 2.12 98 13.59 2.2 48 13.32 3.09 90 14.89 4.31 110 12.9 3.21 104 14.2 3.34 114 13.78 3.01 87 13.38 2.49 102 14.38 2.69 105 14.35 2.26 101 14.78 3.34 60 13.95 2.3 144 14.34 2.95 73 14.64 2.93 89 13.92 2.96 124 13.23 3.42 107 14.58 3.14 87 13.42 3.15 85 13.51 3.86 146 14.15 3.15 163 13.9 3.08 165 12.34 2.09 143 14.22 2.68 58 13.39 2.1 73 14.22 1.89 115 13.44 2.03 89 13.4 2.19 101

Over doses from opioids have captured the national spotlight. Rightly so they kill nearly 30,000 Americas a year and cause more than 1 million hospitalizations. However, the misuse of over-the-counter pain medications (e.g. Tylenol, Advil, Aleve) can cause stomach bleeding, ulcers, liver disease and, in some cases, death. Approximately 80% of Americans use these medications to relieve headaches, backaches, sore muscles, and reduce fever but they are unaware of the dangers if the drugs are not used correctly. A random sample (n=101) of adults were given a questionnaire to ask the question "How often do you use pain medication in one day?". Using the output, histogram, box- whisker plot, and the QQ Plot attached - check the assumption of normality for this data. PainNormalityInformationoutputhistbox 210317.pdf The assumption of normality was checked by comparing the and the median. This suggests that the distribution is slightly The + The is between the acceptable range of -3 and +3.…

sub questions 1,2 and 3 please

1. Let X be an RV with PDF a. Find the mean of X. b. Find the variance of X. f(x) = {¹ -=| - |x| for x < 1 otherwise

*2. Let log Y the median of Y). ~ N (u, o2). Find the distribution of Y and show that P(Y < eH) = 0.5 (i.e., el is

Send data to Excel Observed frequency fo Expected frequency ƒE 2 (fo-fe) ƒE Winter Spring Summer 35 1 ☐ 23 37.50 5.607 44 37.50 Fall 48 П 1.127 1 Total 150 X

3. 1 + x Check whether the following function is a valid pdf? If it is valid, obtain its CDF. If not valid, would scaling by a constant make it valid? If so, make it valid. Obtain its CDF? What is its mean? Variance? ƒ = —exp(-√x)U(x)

Ch. 6.1 CI What sample size is needed to give the desired margin of error in estimating a population proportion with the indicated level of confidence? (16) A margin of error within +/- 1% with 99% confidence. (18) A margin of error within +/- 2% with 95% confidence. An initial small sample has p-hat=0.78

Help  1. Is there a significant difference between Group X and Group Y? How do you know?