The lifetime, X, of a particular integrated circuit has an exponential distribution with rate of ?=0.5 per year. Thus, the density of X is: f(x,?) = ? e−?x for 0 ≤ x ≤ ∞, ? = 0.5 . ? 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. a) What is the expected value of X? b) What is the variance of X? c) What is the standard deviation of X?
The lifetime, X, of a particular integrated circuit has an exponential distribution with rate of ?=0.5 per year. Thus, the density of X is:
f(x,?) = ? e−?x for 0 ≤ x ≤ ∞, ? = 0.5 . ? 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
a) What is the
b) What is the variance of X?
c) What is the standard deviation of X?
d) What is the
e) What is the probability that X is > 5?
f) What is the probability that X is > 10?
g) What is the probability that X > 10 given that X > 5?
h) What is the
Step by step
Solved in 2 steps
