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Question
The following function represents the p.d.f of a.r.v. X
f(x) = `{{:((kx;, "for" 0 < x < 2, "then the value of K is ")),((0;, "otherwise")):}` ______
Options
`3/2`
`1/2`
1
0
Solution
`bb(1/2)`
Explanation:
f(x) is a p.d.f of random variable x.
∴ `int_a^b f(x).dx` = 1
⇒ `int_0^2 kx.dx` = 1
⇒ `k[x^2/2]_0^2` = 1
⇒ `k(2^2/2 - 0)` = 1
⇒ 2k = 1
⇒ k = `1/2`.
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