Applied Statistics and Probability for Engineers, 6th Edition

Published by Wiley
ISBN 10: 1118539710
ISBN 13: 978-1-11853-971-2

Chapter 3 - Section 3-2 - Probability Distributions and Probability Mass Functions - Exercises - Page 69: 3-17


(a) P(X≤2)=1 (b)P(X>-2)=0.8 (c) P(-1$\leq$X$\leq1)$=0.7 (d) P(X ≤-1 or X=2)=0.7

Work Step by Step

Given that, $f( -2)=0.2, f( -1)=0.4,f( 0)=0.1,f( 1)=0.2,f( 2)=0.1,$ this means that for all possible values of x, f(x) ≥ 0, and, P(X=-2)+P(X=-1)+P(X=0)+P(X=1)+P(X=2)=0.2+0.4+0.1+0.2+0.1=1 (a) P(X≤2)=P(X=-2)+P(X=-1)+P(X=0)+P(X=1)+P(X=2) =0.2+0.4+0.1+0.2+0.1=1 (b)P(X>-2)=P(X=-1)+P(X=0)+P(X=1)+P(X=2)=0.4+0.1+0.2+0.1=0.8 (c) P(-1$\leq$X$\leq1)$=P(X=-1)+P(X=0)+P(X=1)=0.4+0.1+0.2=0.7 (d) P(X ≤-1 or X=2)= P(X=-2)+P(X=-1)+P(X=2)=0.2+0.4+0.1=0.7
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