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1 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.

Respuesta :

Answer:

Step-by-step explanation:

Given that you choose at random a real number X from the interval [2, 10].

a) Since this is a contnuous interval with all number in between equally likely

E = probability for choosing a real number is U(2,10)

pdf of E is [tex]\frac{1}{8}[/tex]

b) P(X>5) = [tex]\int\limits^10_5 {1/8} \, dx = \frac{5}{8}[/tex]

[tex]P(5<x<7) = \frac{2}{8} =\frac{1}{4}[/tex]

For

[tex]x^2-12x+35 >0\\(x-5)(x-7)>0\\x<5 or x >7[/tex]

P(X<5 or x>7) = 1-P(5<x<7)

= [tex]\frac{3}{4}[/tex]

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