Math Problem Statement
Assume that X is a continuous random variable with the probability density function (pdf) f(x) = 10e−10x ,0 <x<∞. Also recall in the class that E(g(X)) =∞ −∞g(x)f(x)dx. (a) Verify that f(x) is indeed a pdf (b) Find P(0 <X <10),P(X >5) (c) Find µ= E[X] (d) Find E[(X−µ)2] where µ is found from the previous question
Solution
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Probability Theory
Continuous Random Variables
Probability Density Functions
Expected Value
Variance
Formulas
Probability Density Function (PDF): f(x) = 10e^(-10x)
Expected Value E[X] = ∫ x f(x) dx
Variance E[(X - µ)^2] = E[X^2] - (E[X])^2
Theorems
Expectation Theorem
Variance Formula
Suitable Grade Level
Undergraduate - Probability and Statistics
Related Recommendation
Exponential Distribution PDF: Solving for Probabilities and Thresholds
Find E[X^2] and Var(X) for Exponential Distribution with PDF f(x) = 2e^(-2x)
Mean Value Calculation for PDF: F(x) = 3/5 * 10^5 * x(100 - x)
Calculating Expected Value and Variance for Exponential Distribution f(x) = 4e^(-4x)
Find E[X^2] and Variance of X for a Continuous Random Variable with Exponential PDF