Problem 13E

Resistors labeled 100 Ω have true resistances that are between 80 Ω and 120 Ω. Let X be the mass of a randomly chosen resistor. The probability density function of X is given by

a. What proportion of resistors have resistances less than 90 Ω?

b. Find the mean resistance.

c. Find the standard deviation of the resistances.

d. Find the cumulative distribution function of the resistances.

Solution

Step 1 of 4

Let X be the mass of a randomly selected resistor

The probability density function is given as

, 80<x<120

=0, otherwise

a) By using the given pdf we have to find the probability of the resistors having resistance less than 90

=

=

=0.0625

the probability of the resistors having resistance less than 90 is 0.0625