5.4. The probability density function of X, the lifetime of a certain type of electronic device (measured in hours), is given by10x > 10f)010a. 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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Asked Nov 5, 2019

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5.4. The probability density function of X, the lifetime of a certain type of electronic device (measured in hours), is given by
10
x > 10
f)
0
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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5.4. The probability density function of X, the lifetime of a certain type of electronic device (measured in hours), is given by 10 x > 10 f) 0 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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Step 1

Consider,

The PDF of X:

10
:> 10
7,X
f(x)=
x
(0,x<10
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10 :> 10 7,X f(x)= x (0,x<10

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Step 2

a)

The required probability can be computed as;

10
> 10
f(X)=x
0,x<10
10
P(X 20)
20 -
10
20
1
=-10
1
20
:-10
20
=0.5
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10 > 10 f(X)=x 0,x<10 10 P(X 20) 20 - 10 20 1 =-10 1 20 :-10 20 =0.5

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Step 3

B)

The CDF of X is...

x
P(Xx)=f(x)ds
10
10
x
10
1
0-10
10
1
=-10
x 10
10
=1--
x
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x P(Xx)=f(x)ds 10 10 x 10 1 0-10 10 1 =-10 x 10 10 =1-- x

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