The decibel excess, X, of a landing 747 Jet, has the following cumulative distribution function F: F(x) = 0 for x < 3 and F(x)=

x³6x9

171

for 3 x 6 and F(x) = 1 for x > 6 a) What is the probability density function for X for 3 x 6?

f(x) =

3x²15

171

f(x) = 3x²

6

171

f(x) =

3x²6

171

f(x) =

3x²

171

f(x) = 3x

b) What is the probability that X > 3.5? c) What is the probability X < 3.5 ? d) What is the probability that X > 5 ? e) What is the probability that X > 5.7 ? f) What is the probability that X > 5.7 given that X > 5? g) Calculate the median of X. h) Calculate the expected value of X? i) Calculate the expected value of

X²

? j) Calculate the variance of X? k) What is the probability that X is more than 0.1 below its expected value? l) Add any comments below.

question 02

Swiss is a built-in R data frame giving standardized fertility measure and socio-economic indicators for each of 47 French-speaking provinces of Switzerland at about 1888.. We are interested in some descriptive statistics related to the Agriculture column of swiss. We can access the data directly by using the assignment x <- swiss$Agriculture. (In R use ?swiss for info on this dataset.) Remember: x <- swiss$Agriculture a.Calculate the sample median of x. b. Using the R quantile function, find the .34 quantile of x.(34th percentile) c. Calculate the interquartile range of x using R. d. Calculate the sample mean of x. e. Calculate a 2/47 trimmed mean for x. f. Calculate the sample variance of x. g. Calculate the sample standard deviation of x. h. What proportion of the x values are within 2.0 sample standard deviations from the sample mean i. Calculate the maximum value of x. j. What number do you get if you add up the sum of the squares of the values in x? Add any comments below. question 03

The lifetime X, (time until battery dies) of a battery of a hybrid car from Company T, is normally distributed with a mean = 47 months and a standard deviation = 8.2 months. Suppose that we take a random sample of 63 hybrid cars from company T and determine the lifetime of the battery, in months, for each car chosen. Let M be the sample mean of the 63 lifetime measurements. Let S be the sum of the 63 lifetime measurements. a) What is the probability that X < 50? b) What is the probability that X > 50? c) What is the probability that all of the 63 measurements are greater than 33? d) What is the expected value of S? e) What is the standard deviation of S? f) What is the probability that S-63*47 >10? g) What is the standard deviation of S-63*47 h) What is the expected value of M? i) What is the standard deviation of M? j) What is the probability that M >50? k) What is the standard deviation of 63*M? l) If the probability of X > k is equal to .6, then what is k?