# Probability density function

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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?

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(This problem is from Continuous Random Variables.)

a) P { X>20}

f (x) = 10/ x2

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

= ∫10/ x2 dx = -10 /x

calculating the integral within the limits 20 and infinity

= [- 10 / x ] 20 ∞

= - 10 ( 1 / ∞ - 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 = ∫ f(x) dx = ∫10/ x2 dx calculated ...

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