A system consisting of two components will con- tinue to operate only as long as both components function. Suppose the joint pdf of the lifetimes (months) of the two components in a system is given by f(x, y) = c[10 - (x+y) for x > 0, y > 0, x+ y < 10 a. If the first component functions for exactly 3 months, what is the probability that the sec- ond functions for more than 2 months? b. Suppose the system will continue to work only as long as both components function. Among 20 of these systems that operate independently of each other, what is the probability that at least half work for more than 3 months?

Q12. Suppose we are running gradient descent to fit a logistic regression model with 0 E R*+1. Suggest one way to check whether the learning rate « is set properly and that gradient descent is running correctly.

If 6 - z f(z) = %3D 3+z? find f'(z). f'(z) = %3!

drivers of that Age - ]]], [16 – 17,1,55], [18 - 19,2,30], [20 - 24, 3, A traffic safety organization has compiled data in an urban region of Canada on the rate of non-fatal vehicle injury accidents, y, as a function of the age of the driver, x. The data is shown below. It is assumed that an injury accident affects either the driver or passengers or others external to the vehicle and does not result in death. Age Range of x, Designated Age Driver Category of Driver y, Number of Injury Accidents per 10 million km driven by drivers of that Age 16-17 1 55 18-19 2 30 20-24 3 24 25-29 4 22 30-39 5 14 40-49 6 13 50-59 7 12 60-69 8 10 70-79 9 14 10