Introduction to Probability · Problem 2.2.2

Combinatorics — Grinstead & Snell

Mathematics — Probability · continuous-density-functions

Problem

Suppose you choose a real number

X

from the interval

[2, 10]

with a density function of the form

f(x) = Cx,

where

C

is a constant. (a) Find

C

. (b) Find

P(E)

, where

E = [a, b]

is a subinterval of

[2, 10]

. (c) Find

P(X > 5)

P(X < 7)

, and

P(X^2 - 12X + 35 > 0)