A traffic light at a certain intersection is green 50% of the time, yellow 10% of the time, and red 40% of the time. A car approaches this intersection once each day. Let X represent the number of days that pass up to and including the first time the car encounters a red light. Assume that each day represents an independent trial.

a. Find P(X = 3).

b. Find P(X ≤ 3).

c. Find μ_X.

d. Find σ²_X.