The lifetime, X, of a particular integrated circuit has an exponential distribution with rate of λ=0.5 per year. Thus, the density of X is: f(x,^) = λ ex for 0 ≤ x ≤ ∞, λ = 0.5. λ 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. d) What is the probability that X is greater than its expected value? e) What is the probability that X is > 5? [ f) What is the probability that X is> 10?

The lifetime, X, of a particular integrated circuit has an exponential distribution with rate of λ=0.5 per year. Thus, the density of X is: f(x,^) = λ ex for 0 ≤ x ≤ ∞, λ = 0.5. λ 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. d) What is the probability that X is greater than its expected value? e) What is the probability that X is > 5? [ f) What is the probability that X is> 10?

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

Chapter1: Functions

Section1.2: Functions Given By Tables

Problem 11E: A Troublesome Snowball One winter afternoon, unbeknownst to his mom, a child bring a snowball into...

See similar textbooks

Similar questions

A Troublesome Snowball One winter afternoon, unbeknownst to his mom, a child bring a snowball into the house, lays it on the floor, and then goes to watch T.V. Let W=W(t) be the volume of dirty water that has soaked into the carpet t minutes after the snowball was deposited on the floor. Explain in practical terms what the limiting value of W represents, and tell what has happened physically when this limiting value is reached.
Use the table of values you made in part 4 of the example to find the limiting value of the average rate of change in velocity.
Find the average rates of change of f(x)=x2+2x (a) from x1=3 to x2=2 and (b) from x1=2 to x2=0.
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?
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.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 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? l) Enter any comments in the…
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? d) What is the probability that X is greater 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?
Suppose that a study of a certain computer system reveals that the response time, in seconds, has an exponential distribution with density curve f(x) = (1/3)e(-x/3) for x > 0 and f(x) = 0 otherwise. What is the probability that response time exceeds 5 seconds? What is the probability that response time exceeds 10 seconds?
X, Y follow the exponential distribution with rate parameter lambda = 5.0 P[X >= 5] ? Write P[X+Y <= 14] as an integral
Compare a graph of the normal density function with mean of 0 and standard deviation of 1 with a graph of a normal density function with mean equal to 4 and standard deviation of 1. The graphs would: Have the same height but one would be shifted 4 units to the right. Have no horizontal displacement but one would be flatter than the other. Have no horizontal displacement but one would be steeper that the other.
Find the mean and variance of the gamma distributionusing integration to obtain E(X) and E(X2).[Hint: Express the integrand in terms of a gammadensity.]
While taking a walk along the road where you live, you accidentally drop your glove, but you don't know where. The probability density p(x) for having dropped the glove x kilometers from home (along the road) is p(x)=7e−7x for x≥0 At what distance y from home is the probability that you dropped it within y km of home equal to 0.95?
Suppose the variables Q and W are skewed distributions defined over a limited set of values. What is the probability that W takes on a value between 0.5 and 1.75? What is E(W)? Suppose that the domain of W changes to 0<t<2.5, what happens to the Probability Density Function (PDF)?