Let z ∼ n (0, 1). for a random vector (x1, . . , xn) where n is a positive integer and x1, . . , xn are real-valued random variables, the expectation of (x1, . . , xn) is the vector of elementwise expectations of each random variable and the covariance matrix of (x1, . . , xn) is the n × n matrix whose (i, j) entry is cov(xi , xj ) for all i, j ∈ {1, . . , n}. find the mean and covariance matrix of (z, 1{z > c}) in terms of φ and φ, the standard gaussian pdf and cdf respectively