Consider a random variable X such that P(X= -1) = P(X= 1) = ½
a. Compute E(x)
b. Compute var(x)
c. Compute P(/X-μ/≥1)
d. Show that Chebyshev's inequality is an equality for P(/X-μ/≥1).
a. E(x) = (1/2)*(-1) + (1/2)*(1) = 0
b. var(x) = ((-1 - 0)2 + (1 - 0)2)/2 = 1
c. P(|x - E(x)|>1) = 0, P(|x - E(x)|=1) = 1
d. See c.