Question

The error involved in making a certain measurement is a continuous rv X with the following pdf.

F(x)=       0.09375(4-x^2) −2 ≤ x ≤ 2

                        0                                                      otherwise

(d) Compute P(X < −0.3 or X > 0.3). (Round your answer to four decimal places.)

Answer 1

Answer:

Given,

F(x)=       0.09375(4-x^2) −2 ≤ x ≤ 2

                        0                                                      otherwise

To determine the probability

i.e.,

now consider,

P(X < - 0.3 or X > 0.3) = 1 - P(-0.3 < X < 0.3)

= 1 - integral of (0.09375(4-X^2))dx [limits = -0.3 to 0.3]

= 1 - (0.375 x -0.03125 x^3) [limits -0.3 to 0.3]

= 1 - 0.20625

P(X < - 0.3 or X > 0.3) = 0.7938