Passage question

00:00Est. 2 min

Marks+2.000.00

Passage

Based on the above data, answer the given subquestions. A weather forecaster wants to predict the rainfall in a local area in the month of July. Suppose a random variable

X

represents the amount of rainfall (in inches) in the local area and the PDF of

X

is

f(x)=\{k e^{-x/20},\ 0<x<\infty;\ 0,\ \text{otherwise}\}

.

Question

Find the value of

k

such that

f(x)

is a valid PDF. Hint:

\int e^{-ax}\,dx=-e^{-ax}/a

.

ComprehensionEasy Difficulty06 August 2023