Question

Find k if f(X) is probability density function of X f(x) = kx(1-x); for 0 < x< 1

Answer 1

Answer:

∵ the value of a probability density function over the whole range is equal to

′

1

′

i) ∴∫

0

2

f(x)dx=∫

0

2

kxdx=1

⇒K[

2

x

2

]

0

2

=1

⇒k[

2

4

−0]=1

⇒k×2=1

⇒k=

2

1

ii) P(1<x<2)

∫

1

2

f(x)dx=∫

1

2

2

1

xdx Putting value of k=

2

1

=

2

1

[

2

x

2

]

1

2

=

2

1

[

2

4

−

2

1

]

=

2

1

×

2

3

=

4

3

∴

P(1<x<2)=

4

3