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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

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

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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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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