Twaiting for the emission of a certain radioactive particle has an exponential distribution with rate of ?=0.25 per second. Thus, the density of X is: f(x,?) = ? e−?x for 0 ≤ x ≤ ∞, ? = 0.25 . ? 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
Twaiting for the emission of a certain radioactive particle has an exponential distribution with rate of ?=0.25 per second. Thus, the density of X is:
for 0 ≤ x ≤ ∞, ? = 0.25 . ? 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 probability that X is less than its expected value?
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
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