Hi everyone!

"Let X be a discretely distributed stochastic variable with the probabilitydistribution given in the following table:

The problem:

(attached as picture to the post)

Calculate the expected value of X.

Decide the probabilities:

P(X ≥ 0) and P (X ≥ 0 | X ≤ 1)"

What I have done to solve it so far:

To calculate the expected value of X:

E(x) = (-2 x 0,1) + (-1 x 0,1) + (0 x 0,5) + (1 x 0,2) + (2 x 0,1) = 0,1

To decide the probability of P(X ≥ 0):

0,5 + 0,2 + 0,1 = 0,8

To decide the probability of P(X ≥ 0 | X ≤ 1):

0,5 + 0,2 = 0,7

The last calculation appears to be wrong and I am not sure why. The two first fit with the answer key, but not the last one (0,5 + 0,2 = 0,7).

Could anyone help me? Thank you so much!