Question

Determine k, if the p.d.f of the random variable is given by f(x) = { e , 0 ≤ x ≤ 0, otherwise Find P(0 < x < log√5 ). ​

Answer 1

Answer:

⇒∫01k(1−x2)dx=1

⇒k[x−3x3]01=1

⇒k(1−31)=1

⇒32k=1

⇒k=23

(ii) The distribution function F(x)=∫−∞xf(t)dt

(a) When x∈(−∞,0]

F(x)=∫−∞xf(t)dt=0

(b) When xε(0,1]

F(x)=∫−∞xf(t)dt=∫−∞0f(t)dt+∫0xf(t)dt

=0+23∫0x(1−t2)dt

F(x)=23(x−

Step-by-step explanation:

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