Question

The p.d.f of a random variable x is given by

f(x) = `1/"4a"`, 0 < x < 4a, (a > 0)

= 0, otherwise

and `"P"(x < "3a"/2) = "kp"(x > "5a"/2)` then k = ?

पर्याय

• 1

• `1/4`

• `1/8`

• `1/2`

Answer 1

1

Explanation:

We have p. d. f of a random variable x is given by

f(x) = `1/"4a"`, 0 < x < 4a, (a > 0)

and also, `"P"(x < "3a"/2) = "kp"(x > "5a"/2)`

`=> int_0^("3a"/2) "f"(x) "dx" = "k"int_("5a"/2)^"4a" "f"(x) "dx"`

`=> int_0^("3a"/2) (1/"4a") "dx" = "k" int_("5a"/2)^"4a" (1/"4a") "dx"`

`=> 1/"4a" int_0^("3a"/2) "dx" = "k"/"4a" int_("5a"/2)^"4a" "dx"`

`=> (x)_0^("3a"/2) = "k"(x) _("5a"/2)^"4a"`

`=> ("3a"/2 - 0) = "k"("4a" - "5a"/2)`

`=> "3a"/2 = "k"("3a"/2)`

⇒ k = 1