Can someone explain to me why is $P(Y = 1) = P(X = -1)+P(X = 1)$?
Why is P(Y = 1) the sum of P(X = -1) and P(X= 1)? I don't see how $Y = X^2$ comes into play? I am very new to this stuff.
Can someone explain to me why is $P(Y = 1) = P(X = -1)+P(X = 1)$?
Why is P(Y = 1) the sum of P(X = -1) and P(X= 1)? I don't see how $Y = X^2$ comes into play? I am very new to this stuff.
We have $Y=1$ iff $X^2=1$ iff $X=1$ or $X=-1$.
The only way that $X^2$ can be $1$ is $X=1$ or $X=-1$. The probability that $X=1$ is $0.3$, the probability that $X=-1$ is $0.2$, so the probability that one or the other happens is $0.3+0.2$. You can draw a Venn diagram. Divide the "world" into $3$ non-intersecting pieces, label one of them $X=1$, another $X=-1$, and the third $X=0$. The probability that $X^2=1$ is the sum of the probabilities of the first two pieces.