(1.) An event X has 3 outcomes +1, -1, 0, each occurring with an equal probability. What is the expected value E(X)?

a. 1

b. 0.5

c. 0.33

d. zero

(2.) An event X has 3 outcomes +1, -1, 0, each occurring with an equal probability. What is the expected value E(2X+3)?

a. 3

b. 1.5

c. 1

d. zero

(3.) An event X has 3 outcomes +1, -1, 0, each occurring with an equal probability. What is the value E(X2)?

a. 1

b. 0.66

c. 0.33

d. zero

(4.) An event X has 3 outcomes +1, -1, 0, each occurring with an equal probability. What is the value Var(X)?

a. 1

b. 0.66

c. 0.33

d. zero

(5.) A distribution that is the square of a normal distribution is:

a. chi-squared distribution

b. t-distribution

c. standard normal distribution

d. F-distribution with 'n' degrees of freedom

please explain your answers clearly. thanks