How do you find the value of 'k' in this probability density function?

If X is a continuous function then the total probability of 1 will be the area enclosed from x = 1 to x = 9

i.e. ∫ (k/x) dx....from x = 1 to x = 9

=> k[lnx]..from 1 to 9

so, k[ln9 - ln1] = 1

i.e. kln9 = 1

=> k = 1/ln9...i.e. 0.455 to 3 s.f.

:)>

WEll,

X is a continuous random variable having the probability density function

f(x) = k/x for 1≤x≤ 9

f(x) = 0 elsewhere

where k is a constant.

f is a pdf if and only if f(x) >= 0 for any x, and Integral (on R) f(x) dx = Int( 1 to 9) f(x) dx= 1

so

J = Int ( 1 to 9) (k/x) dx = 1

k [ lnx ] (between 1 and 9) = 1

k(ln9 - ln1) = 1

3kln3 = 1

finally : k = 1/ln9

and you can get your calc. for the decimals...

hope it' ll help !!