Suppose X and Y are two resistors whose tolerances form Independent random varia

Question

Suppose X and Y are two resistors whose tolerances form Independent random variables The resistors are placed in series, so the total resistance Z = Z + Y. The PDFs for X and Y are f_X (x) = {1/20, 90 lessthanorequalto x lessthanorequalto 110 and f_Y (y) = {1/10, 45 lessthanorequalto x lessthanorequalto 55 0, otherwise 0, otherwise a. Find the probability density function for Z. b. Find the mean of Z. c. Find the second moment, variance and standard deviation of Z. d. Is the variance of 2 greater or less than the variance of another resistor W with the PDF f_W (W) = {1/30, 135 lessthanorequalto x lessthanorequalto 165 0, otherwise

Explanation / Answer

a) z=x+y

pdf(x) = 1/20 ; <90<x<110 , 0 otherwise

pdf(y) = 1/10 ; <45<y<55 , 0 otherwise

pdf(z) = 1/20 ; <90<x<110 , 1/10 ; <45<y<55 ,0 otherwise

Explanation: probability density function of z will take into account the pdfs of both x and y i.e. whether it falls in the regionof x or y or none.

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