Question

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.

Answer 1

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 $\frac{1}{8}$

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

$P(5$

For

$x^2-12x+35 >0\\(x-5)(x-7)>0\\x7$

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

= $\frac{3}{4}$