Mathematics, 10.03.2020 00:46 paulitaaustin
Resistors labeled 100 have tue resistances that are between 80 and 120. Let X be the mass of randomly chosen resistor. The probability desnsity function of X is given by:
f(x)= {x-80/ 800, 80< x 120 and 0, otherwise
a. what proportion of resistors have resistances less than 90?
b. find the mean resistance.
c. find the standard deviation of the resistances.
d. find the cumulative distribution function of the resistances.
Answers: 3
![\int\limits^{90}_{80} {\frac{x-80}{800} } \, dx \\\\=\frac{1}{800} [0.5x^2- 80x]|^{90}_{80}\\\\=\frac{1}{800} [0.5(90)^2- 80(90)-(0.5(80)^2- 80(80))]](/tpl/images/0539/3779/1820b.png)
![\int\limits^{120}_{80} {xf(x)} \, dx = \int\limits^{120}_{80} {x\frac{x-80}{800} } \, dx\\\\= \frac{1}{800} \int\limits^{120}_{80} {x^2-80x} \, dx \\\\= \frac{1}{800} \times [\frac{x^3}{3} -\frac{80x^2}{2} ]|^{120}_{80}](/tpl/images/0539/3779/34eee.png)
![\int\limits^x_{80} {f(x)} \, dx = \int\limits^x_{80} {\frac{x-80}{800} } \, dx \\\\=\frac{1}{800} [0.5 x^2 - 80x]|^x_{80}](/tpl/images/0539/3779/2ce21.png)
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