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cerna
15.10.2020 •
Mathematics
The thickness of photoresist applied towafers in a semiconductor manufacturing at a particular location onthe wafer is uniformly distributed between 0.2050 and 0.2150micrometers.(a) Determine the cumulative distributionfunction of photoresist thickness.(b) Determine the proportion of wafers that exceeds0.2125 micrometers in photoresist thickness.(c) What thickness is exceeded by 10% of thewafers?(d) Determine the mean and variance of photoresistthickness.
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Ответ:
a
b
c
d
Mean![\mu = 0.21](/tpl/images/0806/8183/3d1ac.png)
Variance![\sigma ^2 = 0.0000083](/tpl/images/0806/8183/92bec.png)
Step-by-step explanation:
From the question we are told that
The thickness of photoresist follows a uniform distribution
So
Generally the probability density function is mathematically represented as
=>![F(x) = \left \{ 100 , 0.2150< x < 0.2150](/tpl/images/0806/8183/c9fee.png)
Generally the cumulative distribution function is
Here
means the lower limit which in this case is 02050
So
=>![f(x)=100 [ x ] | \left \ x} \atop {0.2050}} \right.](/tpl/images/0806/8183/e1c44.png)
=>![f(x)= 100 [x - 0.2050]](/tpl/images/0806/8183/79add.png)
Generally the proportion of wafers that exceeds 0.2125 is mathematically represented as
=>![P(X 0.2125) = 1- 100[0.2125 - 0.2050]](/tpl/images/0806/8183/dbac4.png)
=>![P(X 0.2125) = 0.25](/tpl/images/0806/8183/8c4c9.png)
Generally the thickness which is exceeded by 10% of the wafers is mathematically represented as
=>![1 - F(a) = 0.10](/tpl/images/0806/8183/3bc60.png)
=>![1 -100 (a - 0.2050) = 0.10](/tpl/images/0806/8183/5d409.png)
=>![100(a -0.2050) = 0.90](/tpl/images/0806/8183/1b03f.png)
=>![a - 0.2050 = 0.009](/tpl/images/0806/8183/ab119.png)
=>![a = 0.2140](/tpl/images/0806/8183/4df25.png)
Generally the mean is mathematically represented as
=>![\mu = 0.21](/tpl/images/0806/8183/3d1ac.png)
Generally the variance is mathematically represented as
=>![\sigma ^2 = 0.0000083](/tpl/images/0806/8183/92bec.png)
Ответ:
The answer is 80 because 10x8 is 80 and the nearest 10 means it need to have a 0 behind so it is 80