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: 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: 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:
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 (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?
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 median of X?
Definition Definition Middle value of a data set. The median divides a data set into two halves, and it also called the 50th percentile. The median is much less affected by outliers and skewed data than the mean. If the number of elements in a dataset is odd, then the middlemost element of the data arranged in ascending or descending order is the median. If the number of elements in the dataset is even, the average of the two central elements of the arranged data is the median of the set. For example, if a dataset has five items—12, 13, 21, 27, 31—the median is the third item in ascending order, or 21. If a dataset has six items—12, 13, 21, 27, 31, 33—the median is the average of the third (21) and fourth (27) items. It is calculated as follows: (21 + 27) / 2 = 24.
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