Expected Value with Parameter p

Question

The random variable X has the following probability distribution:

P[X=-1]= (1-p)/2

P[X=0]= 1/2

P[X=1]= p/2

The parameter p satisfies the inequality $0 < p < 1$.

Find the expected value and variance of X.

Do I need to try and solve for p before calculating? I have already multiplied the values for X by their probabilities and I ended up with E[X]=(-1/2)+p. Can anyone confirm if this is correct?

Answer 1

$$\mathbb{E}X=\frac{1-p}{2}\times\left(-1\right)+\frac{1}{2}\times0+\frac{p}{2}\times1=\dots$$

$$\mathbb{E}X^{2}=\frac{1-p}{2}\times\left(-1\right)^{2}+\frac{1}{2}\times0^{2}+\frac{p}{2}\times1^{2}=\dots$$

$$\text{Var}X=\mathbb{E}X^{2}-\left(\mathbb{E}X\right)^{2}=\dots$$

Help yourself.

Your original solution (before your edit) $\mathbb{E}X=\frac{1}{2}+p$ is not correct.

Answer 2

E(X) is correct. And the variance is $Var(X)=E(X^2)-\left[ E(X) \right] ^2$.