The lifetime, in years, of a certain type of pump is a random variable with probability density function:

f(x)= {64/(x+2)^5 x>0
0 x<=0}

a. What is the probability that a pump lasts more than two years?
b. What is the probability that a pump lasts between two and four years?
c. Find the mean lifetime.
d. Find the variance of the lifetimes.
e. Find the cumulative distribution function of the lifetime.
f. Find the median lifetime.
g. Find the 60th percentile of lifetimes.

Analyze the data sets below. data set a 25,25,25,26,26,26,27,28,28,29,30,31,31,32,33,33,34,35,35,35 data set b 25,25,25,26,26,26,26,27,27,27,27,28,28,29,29,30,31,31,32,34 which of the following statement are true? select all that apply. a. data set a is relatively symmetric and data set b is skewed left. b.the means of the data sets are within 3 units from eachother. c.the data sets have the same standard deviation. d.the mean of data set a is 27.95 and the mean of data set b is 30. e. the data set b has a higher standard deviation than data set a. f. the mean and median of data set a are close in value.

Let f(x) = 3 − x . find the average rate of change of f(x) from x = a to x = a + h and simplify your answer so that no single factor of h is left in the denominator.

Look at this pattern ; 1,4,9, number 10000 belongs in this pattern . what’s the place of this number?