Suppose a random variable X has the following discrete probability distribution:

x P(x)

0 0.2

1 0.0

2 0.8

1) The mode of the distribution is:

a) 0 b) 1 c) 1.6d) 2e) Not enough information.

2)The expected value ofXis:

a) 0 b)0.5 c)1 d)2 e)1.6

3) The variance of the distribution is:

a) 0.64b) 0.8 c) 1.373 d) 1.172 e) 1.8

I need explanation and clear breakdown of the calculation. Thank you!