5. 0.56/4 points 14 Submissions Used My Notos Ask Your T A consumer organization

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5. 0.56/4 points 14 Submissions Used My Notos Ask Your T A consumer organization that evaluates new automobiles customarily reports the number of major defects in each car examined. Let X denote the number of major defects in a randomly selected car of a certain type. The cdf of X is as follows: 0.04 0 0.19 1 0,34 2 0.54 3 0.92 4 0.96 5 F(x)- Calculate the following probabilities directly from the cdf: (Round to two decimal places.) (a) F(2), that is, PX S 2) 0.34 (b) P(x> 3) 0.46 (c) P(2sXš 5) (d) P(2

Explanation / Answer

P(x=0) =0.04

P(x 1) =P(x=0) +P(x=1)

0.19 =0.04+P(x=1)

so P(x=1) =0.19-0.04 =0.15

P(x 2) =P(x 1)+P(x=2)

0.34 =0.19 +P(x=2)

0.34-0.19 =P(x=2)

P(x=2) =0.15

P(x 3) =P(x 2)+P(x=3)

0.54 =0.34 +P(x=3)

P(x=3) =0.54-0.34 =0.20

P(x 4) =P(x 3) +P(x=4)

0.92 =0.54 +P(x=4)

P(x=4) =0.92-0.54 =0.38

P(x 5) =P(x 4) +P(x=5)

0.96 =0.92 +P(x=5)

P(x=5) =0.96-0.92 =0.04

P(x 6) =P(x 5) +P(x=6)

1 =0.96 +P(x=6)

P(x=6) =1-0.96 =0.04

part c) P(2 x 5) =P(x=2) +P(x=3) +P(x=4) +P(x=5)

                                             = 0.15+0.20+0.38+0.04 =0.77

part d) P(2<x<5) =P(x=3) +P(x=4)

                              =0.20+0.38 =0.58

part e)

x             0             1             2             3             4             5             6

p(x)        0.04       0.15       0.15       0.20       0.38       0.04       0.04

part f)

E(x) ==xp(x) =0*0.04 + 1*0.15 2*0.15 +3*0.20 4*0.38 +5*0.04 +6*0.04 =3.01

V(x) =^2=x^2p(x)^2 =[0^2 *0.04 + 1^2 *0.15 2^2 *0.15 +3^2 *0.20 4^2 *0.38 +5^2 *0.04 +6^2 *0.04] -3.01^2

                                             = 11.07 -9.0601

                                             =2.01

SD(x) = =sqrt(2.0099) =1.42

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