Consider a random variable,X,with Uniform density over the range 0 to 1. Given that X is at least 0.4,find the probability that X is less than 0.6.
A)0.33
B)0.60
C)0.40
D)0.67
E)0.00

Question

Consider a random variable,X,with Uniform density over the range 0 to 1.  Given that X is at least 0.4,find the probability that X is less than 0.6.
A)0.33 
B)0.60 
C)0.40 
D)0.67 
E)0.00

Quizplus · Accepted Answer

Given that $X$ is at least $0.4$, we know that the density of $X$ is 1 for $0.4\leq X\leq 1$. We need to find the probability that $X$ is less than $0.6$ given that $X\geq 0.4$.

This is equivalent to finding $P(0.4\leq X<0.6)$ divided by $P(X\geq 0.4)$.

$P(0.4\leq X<0.6)$ is the area of a rectangle with base $0.2$ and height $1$, which is $0.2$.

$P(X\geq 0.4)$ is the area of a rectangle with base $0.6$ and height $1$, which is $0.6$.

Therefore, the probability that $X$ is less than $0.6$ given that $X\geq 0.4$ is $\dfrac{0.2}{0.6} = 0.33$.

Hence, the answer is A) 0.33.

Consider a Random Variable,X,with Uniform Density Over the Range 0