Suppose you choose at random a real number X from the interval [2, 10].(a) Find the density function f(x) and the probability of an event E for this experiment, where E is a subinterval [a, b] of [2, 10].(b) From (a) find the probability that X > 5, that 5 < X < 7, and that X2−12X +35 >0.

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Asked Nov 10, 2019
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Suppose you choose at random a real number X from the interval [2, 10].

(a) Find the density function f(x) and the probability of an event E for this experiment, where E is a subinterval [a, b] of [2, 10].
(b) From (a) find the probability that X > 5, that 5 < X < 7, and that X2−12X +35 >0.

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Expert Answer

Step 1

First find density function f(x)  

 

Let X follows Uniform distribution

 

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asXsb f(x)=b-a elsewhere

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Step 2

 

X lies in the interval [2, 10]

 

The density function of X is:

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1 2s Xs10 f(x)10-2 elsewhere 2sXs10 8 elsewhere

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Step 3

The probability of an event E...

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P([a.b])=d 8 1 (b-a) 8 if b 10 and a 2 then (10-2) 8 =1

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