The distance, X, between consecutive anomalies on long cable has an exponential distribution with mean 12 meters. Thus, the density of X is:: f(x,?) = ? e−?x for 0 ≤ x ≤ ∞, ? = 1 12 . ? is what R calls rate. Hint: This is a problem involving the exponential distribution. Knowing the parameter ? for the distribution allows you to easily answer parts a ,b ,c and use the built-in R functions for the exponential distribution (dexp(), pexp(), qexp()) for other parts . Or (not recommended) you should be able to use the R integrate command with f(x) defined as above or with dexp() for all parts. ) What is the probability that X is larger than its expected value? e) What is the probability that X is > 13? f) What is the probability that X is > 14? g) What is the probability that X > 14 given that X > 13? h) What is the median of X?
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
The distance, X, between consecutive anomalies on long cable has an exponential distribution with mean 12 meters. Thus, the density of X is::
for 0 ≤ x ≤ ∞, ? =
| 1 |
| 12 |
. ? is what R calls rate.
Hint: This is a problem involving the exponential distribution. Knowing the parameter ? for the distribution allows you to easily answer parts a ,b ,c and use the built-in R
) What is the
e) What is the probability that X is > 13?
f) What is the probability that X is > 14?
g) What is the probability that X > 14 given that X > 13?
h) What is the median of X?
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 3 images
