Probability density

Question

Hello

 

Could someone give me the answer to this question please

I have just started a course on big data

 

(3/k is a fraction) 

Find k such that f(x) = 3/k x⁴ is a probability density function for x ∈ [2, 3]?

Thank you in advance

Answer 1

The definite integral of a PDF over its domain [2,3] must be 1.

 

So you require that ∫₂³(3/k)x⁴dx = 1 ...I'm assuming that the 4th power of x is a factor in the integrand.

 

Antiderivative F(x) = (3x⁵)/(5k) and you need to have F(3) - F(2) = 1 ... (evaluating definite integral on [2,3])

i.e. 3/(5k)[3⁵-2⁵] = 1  or  k = (3/5)(211)