The random variable $x$ $x$ is known to be uniformly distributed between 1.0 and 1.5. What is $P (1.20 \leq x \leq 1.5)$ $P(1.20<=x<=1.5)$ ?

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Answer 1 · 2017-08-30T08:32:36

$P (1.2 \leq X \leq 1.5) = 0.6$ $P( 1.2<= X <= 1.5)=0.6$

The diagrams below represent the Uniform distribution in general, and the probability required

enter image source here

the first diagram shows this particular uniform distribution.

The area of the rectangle has to be

$1$ $1$

so we have;

$k (1.5 - 1.0) = 1$ $k(1.5-1.0)=1$

$:.k=1/0.5=2$

For

$P( 1.2<= X <= 1.5)$

we require the area of the shaded part of the second diagram

$P( 1.2<= X <= 1.5)=k(1.5-1.2)$

$=2xx0.3=0.6$

The random variable xxx is known to be uniformly distributed between 1.0 and 1.5. What is P(1.20<=x<=1.5) P(1.20≤x≤1.5)P(1.20<=x<=1.5) ?