manufacturing. Let X- the number of defective pixels per screen. The numbers of
ID: 3065977 • Letter: M
Question
manufacturing. Let X- the number of defective pixels per screen. The numbers of defects per screen along with the associated probability are listed in the table below 2. For warranty purposes, analysts want to model the number of defects on a screen of the new tablet they ars smnndo Number of Probability Sereen (3)0.95 OSTTIMS 0.04 0.008 ili : // 0 I 12 Idimczo zid) no emald0 0wara hort od, ol eivrais 1i104 dano chnolo Compute the expected value of the number of defects per screen AND calculate the standard deviation of the number of defects per screen.Explanation / Answer
Solution:
Expected value = E(X) = XP(X)
Variance = X^2*P(X) – [E(X)]^2
Standard deviation = sqrt(variance)
Table calculations are provided below:
X
P(X)
XP(X)
X^2*P(X)
0
0.95
0
0
1
0.04
0.04
0.04
2
0.008
0.016
0.032
3
0.002
0.006
0.018
4
0
0
0
Total
1
0.062
0.09
Expected value = E(X) = XP(X) = 0.062
X^2*P(X) = 0.09
Variance = X^2*P(X) – [E(X)]^2
Variance = 0.09 – (0.062)^2 = 0.086156
Standard deviation = sqrt(0.086156) = 0.293523423
X
P(X)
XP(X)
X^2*P(X)
0
0.95
0
0
1
0.04
0.04
0.04
2
0.008
0.016
0.032
3
0.002
0.006
0.018
4
0
0
0
Total
1
0.062
0.09
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