Question

The pdf of a random variable x is f(x)=k(x-1)(2-x) for[1,2]. what is the value of k?​

Answer 1

Answer:

Step-by-step explanation:

(i) Since f(x) is a p.d.f. ∫

−∞

∞

​

f(x)dx=1

⇒∫

0

1

​

k(1−x

2

)dx=1

⇒k[x−

3

x

3

​

]

0

1

​

=1

⇒k(1−

3

1

​

)=1

⇒

3

2k

​

=1

⇒k=

2

3

​