# Probability density function

4. The probability density function if X, the lifetime of a certain type of electronic device (measured in hours} is given by:

f(x) =

10/x^2 for x>10

and

=0 for x<=10

(a) Find P {X > 20}

(b) What is the cumulative distribution function of X?

(c) What is the probability that of 6 such types of devices at least 3 will function for at least 15 hours? What assumptions are you making?

{see attachment}

Â© BrainMass Inc. brainmass.com March 4, 2021, 6:14 pm ad1c9bdddfhttps://brainmass.com/statistics/probability-density-function/probability-density-function-36653

#### Solution Preview

See attached file

(This problem is from Continuous Random Variables.)

a) P { X>20}

f (x) = 10/ x2

P (X>20) = âˆ« f(x) dx = âˆ«10/ x2 dx with the limits 20 and infinity

= âˆ«10/ x2 dx = -10 /x

calculating the integral within the limits 20 and infinity

= [- 10 / x ] 20 âˆž

= - 10 ( 1 / âˆž - 1/20 ] = - 10 ( 0 - 0.05 ) = 10 * 0.05 = 0.5

Answer: P { X>20}= 0.5

b) cumulative distribution function of X

F (x) = cumulative distribution function of X = âˆ« f(x) dx = âˆ«10/ x2 dx calculated ...

#### Solution Summary

The expert finds probability, cumulative distribution function.