what-is-P-x-gt-1-if-x-has-a-PDF-of-f-x-1-4-2-lt-x-lt-2-0-elsewhere-

Question Number 86668 by jagoll last updated on 30/Mar/20

what is P (∣ x ∣ > 1) if x has a PDF of

f (x) = {\begin{cases} \frac{1}{4}, - 2 < x < 2 \\ 0, elsewhere \end{cases}

Commented by john santu last updated on 30/Mar/20

\Rightarrow P (x < - 1 \cup x > 1)

= \int_{- 2}^{- 1} f (x) dx + \int_{1}^{2} f (x) dx

= \underset{- 2}{\int^{- 1}} \frac{1}{4} dx + \underset{1}{\int^{2}} \frac{1}{4} dx

= \frac{1}{4} [- 1 + 2] + \frac{1}{4} [2 - 1]

= \frac{1}{2}