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1. Let Random variable X represent f times the number we throw a dice: What we 1 2 3 4 5 6 see on dice f 2f 3f 4f P(X=x) 1/6 1/6 1/6 1/6 a) What if the expected value and variance of X? b) What is the expected value and variance of 3X? c) What is the expected value and variance of X+X+X? X 5f 1/6 6f 1/6

1. Let Random variable X represent f times the number we throw a dice: What we 1 2 3 4 5 6 see on dice f 2f 3f 4f P(X=x) 1/6 1/6 1/6 1/6 a) What if the expected value and variance of X? b) What is the expected value and variance of 3X? c) What is the expected value and variance of X+X+X? X 5f 1/6 6f 1/6

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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1. Let Random variable X represent f times the number we throw a dice: What we 2 4 5 6 see on dice 1 X 3 f 2f 3f P(X=x) 1/6 1/6 1/6 a) What if the expected value and variance of X? b) What is the expected value and variance of 3X? c) What is the expected value and variance of X+X+X? 4f 1/6 5f 1/6 6f 1/6 An industrial chemical that will retard the spread of fire in paint has been developed. The local sales representative has estimated, from past experience, that 48+15f% (round to integer) of the sales calls will result in an order. (a) What is the probability that the first order will come on the fourth sales call of the day? (b) If eight sales calls are made in a day, what is the probability of receiving exactly six orders? (c) If four sales calls are made before lunch, what is the probability that one or fewer results in an order?
Transcribed Image Text:1. Let Random variable X represent f times the number we throw a dice: What we 2 4 5 6 see on dice 1 X 3 f 2f 3f P(X=x) 1/6 1/6 1/6 a) What if the expected value and variance of X? b) What is the expected value and variance of 3X? c) What is the expected value and variance of X+X+X? 4f 1/6 5f 1/6 6f 1/6 An industrial chemical that will retard the spread of fire in paint has been developed. The local sales representative has estimated, from past experience, that 48+15f% (round to integer) of the sales calls will result in an order. (a) What is the probability that the first order will come on the fourth sales call of the day? (b) If eight sales calls are made in a day, what is the probability of receiving exactly six orders? (c) If four sales calls are made before lunch, what is the probability that one or fewer results in an order?
Expert Solution
Step 1

given data

x p(x=X) x*p(x) x2 * p(x)
f 1/6 f/6 f2
2f 1/6 2f/6 4f2/6
3f 1/6 3f/6 9f2/6
4f 1/6 4f/6 16f2/6
5f 1/6 5f/6 25f2/6
6f 1/6 6f/6 36f2/6
    Σx*p(x) = 3.5f Σx2*p(x) = 15.1667f2
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