Calculate the specified probability -Suppose that $A$ is a random variable. Also suppose that $P ( T a ) = P ( T

Question

Calculate the specified probability
-Suppose that $A$ is a random variable. Also suppose that $P ( T > a ) = P ( T < - a ) = x$, and that $P ( 0 < T \leq$ a ) $= y$. Find $P ( - a \leq T \leq 0 )$ in terms of $x$ and $y$.  
A)$y$
B) $1 - 2 x - y$
C) $1 - y$
D) $1 - ( 2 x - y )$

Quizplus · Accepted Answer

The total probability is 1, and the event space is divided into four non-overlapping regions: $P(T > a) = x$, $P(T < -a) = x$, $P(0 < T \leq a) = y$, and $P(-a \leq T \leq 0)$, which we want to find. Adding the probabilities of the first three regions gives $2x + y$, so the probability of the fourth region is $1 - (2x + y)$, which simplifies to $1 - 2x - y$.

Calculate the Specified Probability -Suppose That AAA Is a Random Variable P(T>a)=P(T<−a)=xP ( T > a ) = P ( T < - a ) = xP(T>a)=P(T<−a)=x

Calculate the Specified Probability
-Suppose That $A$ Is a Random Variable $P ( T > a ) = P ( T < - a ) = x$