a) Using the f(x) above and the R integrate function calculate the expected value of X. b) Using the f(x) above and the R integrate function calculate the expected value of x4.1 c) Using the dexp function and the R integrate function calculate the expected value of X. d) Using the pexp function find the probability that 2 ≤ x ≤ 4.1 | e) Calculate the probability that X > 1 by using the pexp function f) Calculate the probability that X is at least 1 greater than its expected value. Use the pexp function where

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter9: Multivariable Calculus
Section9.1: Functions Of Several Variables
Problem 34E: The following table provides values of the function f(x,y). However, because of potential; errors in...
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X is a random variable with an exponential distribution with rate λ = 0.4 Thus the pdf of X is f(x) = ex for 0 ≤ x where λ = 0.4
a) Using the f(x) above and the R integrate function calculate the expected value of X.
b) Using the f(x) above and the R integrate function calculate the expected value of x4.1.
c) Using the dexp function and the R integrate function calculate the expected value of X.
d) Using the pexp function find the probability that 2 ≤ x ≤ 4.1 |
e) Calculate the probability that X > 1 by using the pexp function
f) Calculate the probability that X is at least 1 greater than its expected value. Use the pexp function
g) Copy your R script for the above into the text box here.
Transcribed Image Text:X is a random variable with an exponential distribution with rate λ = 0.4 Thus the pdf of X is f(x) = ex for 0 ≤ x where λ = 0.4 a) Using the f(x) above and the R integrate function calculate the expected value of X. b) Using the f(x) above and the R integrate function calculate the expected value of x4.1. c) Using the dexp function and the R integrate function calculate the expected value of X. d) Using the pexp function find the probability that 2 ≤ x ≤ 4.1 | e) Calculate the probability that X > 1 by using the pexp function f) Calculate the probability that X is at least 1 greater than its expected value. Use the pexp function g) Copy your R script for the above into the text box here.
Suppose X has a standard normal distribution. The pnorm(), dnorm(), and qnorm() functions should be useful in the following. Remember, if X has a standard normal distribution then E(X) = 0 and
Var(X)=1.
a) What is the expected value of
b) What is the variance of x-2 ? [
x-2 ? [
= + ? [
c) Using R, find the expected value of
d) Using R, calculate the probability X < -2.01)
e) Using R, calculate the probability that 1.1 < X < 1.21
f) Using R, calculate the probability that -2.2 < 2x-2 < -1.7
g) If the probability that X < t = .64 then what is t?
h) Copy your R script for the above into the text box here.
Transcribed Image Text:Suppose X has a standard normal distribution. The pnorm(), dnorm(), and qnorm() functions should be useful in the following. Remember, if X has a standard normal distribution then E(X) = 0 and Var(X)=1. a) What is the expected value of b) What is the variance of x-2 ? [ x-2 ? [ = + ? [ c) Using R, find the expected value of d) Using R, calculate the probability X < -2.01) e) Using R, calculate the probability that 1.1 < X < 1.21 f) Using R, calculate the probability that -2.2 < 2x-2 < -1.7 g) If the probability that X < t = .64 then what is t? h) Copy your R script for the above into the text box here.
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