A continuous random variable X has density f(x)=0.25 for 1 x5 and zero otherwise. What is P(X4)?

GATE 2016 CE (CE1) – Question 36

Engineering Mathematics · Probability and Statistics: Random variables, Poisson and Normal distributions, linear regression · 2 marks · Multiple choice

A continuous random variable X has density $f(x)=0.25$ for $1\le x\le5$ and zero otherwise. What is $P(X\le4)$?

$3/4$
$1/2$
$1/4$
$1/8$

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Show answer and explanation

Correct answer: (A) $3/4$

Explanation

The uniform density is1/(5−1)=1/4. The interval from1 to4 has length3, so the required probability is3/4=0.75. Endpoint inclusion does not matter for a continuous distribution. Thus **0.75, A**.