The probability density function of x is given as f(x) = ae^-x/5 for x > 0. The value of a is ? (a) 0·5 (b) 0·3 (c) 0·2 (d) 0·1

Thank you. Please help. Is it by taking the integral value = 1?

1 Answer
Dec 3, 2017

a=0.2

Explanation:

pdf" "f(x)=ae^(-x/5), a>0

for a pdf

int_(all" " x)f(x)=1

:.int_0^ooae^(-x/5)dx=1

Lim_(trarroo)int_0^tae^(-x/5)dx=1

Lim_(trarroo)[-5ae^(-x/5)]_0^t=1

Lim_(trarroo)[-5ae^(-x/5)]^t-[-5ae^(-x/5)]_0=1

0--5ae^0=1

=>5a=1

:.a=1/5=0.2