There are two traffic lights on a commuter's route to and from work. Let X1 be the number of lights at which the commuter must stop on his way to work, and X2 be the number of lights at which he must stop when returning from work. Suppose that these two variables are independent, each with the pmf given in the accompanying table (so X1, X2 is a random sample of size n = 2). Can you help me with 3 and 4? ### Discrete Probability Distribution#### Given Probability Distribution for \( X_1 \)- **Values of \( x_1 \):** 0, 1, 2- **Probability \( p(x_1) \):** - \( P(x_1 = 0) = 0.4 \) - \( P(x_1 = 1) = 0.3 \) - \( P(x_1 = 2) = 0.3 \)**Mean (\( \mu \)) and Variance (\( \sigma^2 \))**:- \( \mu = 0.9 \)- \( \sigma^2 = 0.69 \)#### Task(a) Determine the probability mass function (pmf) of \( T_0 = X_1 + X_2 \).#### Probability Distribution for \( T_0 \)- **Values of \( t_0 \):** 0, 1, 2, 3, 4- **Probability \( p(t_0) \):** - \( P(t_0 = 0) = 0.16 \) ✔️ - \( P(t_0 = 1) = 0.24 \) ✔️ - \( P(t_0 = 2) = 0.33 \) ✔️#### ExplanationIn the given distributions, the probabilities for \( t_0 = 0 \), \( t_0 = 1 \), and \( t_0 = 2 \) are specified with check marks, indicating these values are confirmed. Additional probability values for \( t_0 = 3 \) and \( t_0 = 4 \) need to be determined to complete the distribution.

There are two traffic lights on a commuter's route to and from work. Let X1 be the number of lights at which the commuter must stop on his way to work, and X2 be the number of lights at which he must stop when returning from work. Suppose that these two variables are independent,