Answered: Twaiting for the emission of a certain…

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter4: Exponential Functions

Section4.4: Modeling Nearly Exponential Data

Problem 3E: Special Rounding Instructions For this exercise set, round all regression parameters to three...

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Question

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?

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