Question

The pdf of a continuous r.v.X is given by f(x) = `x/8`, 0 < x < 4 = 0, otherwise, then P(X ≤ 2) is ______.

विकल्प

• \[\frac{1}{4}\]

• \[\frac{5}{16}\]

• \[\frac{9}{16}\]

• \[\frac{7}{16}\]

Answer 1

The pdf of a continuous r.v.X is given by f(x) = `x/8`, 0 < x < 4 = 0, otherwise, then P(X ≤ 2) is \[\frac{1}{4}\].

Explanation:

We have,

f(x) = `{(x/8","  0 < x < 4),(0 ","  "otherwise"):}`

P(X ≤ 2) = `int_0^2`f(x) dx

P(X ≤ 2) = `int_0^2 x/8 "dx" = [x^2/16]_0^2 = 4/16 = 1/4`