Download presentation

Presentation is loading. Please wait.

Published byAlex Marton Modified over 2 years ago

1
E(X 2 ) = Var (X) = E(X 2 ) – [E(X)] 2 E(X) = The Mean and Variance of a Continuous Random Variable In order to calculate the mean or expected value of a continuous random variable, we must multiply the probability density function f(x) with x before we integrate within the limits. To calculate the variance, we need to find E(X 2 ) since

2
Example The continuous random variable X is distributed with probability density function f(x) where f(x) = 6x(1-x) is 0 ≤ x ≤ 1 a) Calculate the mean and variance of X. b) Deduce the mean and variance of (i)Y = 10X – 3 (ii)Z = 2(3 – X) 5 c)Evaluate E(5X 2 – 3X + 1)

3
a)Calculate the mean and variance of X. f(x) = 6x(1-x) = 6x – 6x 2 E(X) =

4
Var (X) = E(X 2 ) – [E(X)] 2 E(X 2 ) = Var (X) =

5
b)Deduce the mean and variance of (i) Y = 10X – 3 (ii) Z = 2(3 – X) 5 (i) E(Y) = E(10X – 3) =10E(X) – 3 =2 6 – 2E(X) = 5 (ii) E(Z) = E 6 – 2X = 5 5 6 – 2 x 1 = 5 5 2 10 x 1 – 3 = 2 1 Var(Z) = Var 6 – 2X = 5 5 2 2 x Var (X) = 5 1. 125 Var(Y) = Var(10X – 3) =10 2 Var(X) =5100 x 1 = 20 2 2 x 1 = 5 20

6
c) Evaluate E(5X 2 – 3X + 1) E(5X 2 – 3X + 1) = 5E(X 2 ) – 3E(X) + 1 = 5 x 3 - 3 x 1 + 1 = 10 2 1 Exercise 1.4 Mathematics Statistics Unit S2 - WJEC Homework 11 Homework 12

Similar presentations

OK

Chapter 7 Lesson 7.4a Random Variables and Probability Distributions 7.4: Mean and Standard Deviation of a Random Variable.

Chapter 7 Lesson 7.4a Random Variables and Probability Distributions 7.4: Mean and Standard Deviation of a Random Variable.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on mauryan architecture Download ppt on use of mathematics in daily life Ppt on total internal reflection fluorescence Ppt on marine ecosystem Ppt on accounting standard 13 Maths ppt on surface area and volume for class 10 Ppt on 4 stroke petrol engine Ppt on electric meter testing software Ppt on depth first search example Ppt on condition based maintenance programs