Transition matrix

Exercise 8 (#1.22). Let v be a measure on a o-field F on ? and f and g be Borel functions with respect to F. Show that (i) if f fdy exists and a e R, then [(af)dy exists and is equal to a ] fdy; (ii) if both / fdu and / gdy exist and f fdu + f gdy is well defined, then (f + g)dv exists and is equal to ] fdy + ] gdv. Note. For integrals in calculus, properties such as J(af)dy =a f fdy and [(f + g)dv / fdy + / gav are obvious. However, the proof of them are complicated for integrals defined on general measure spaces. As shown in this exercise, the proof often has to be broken into several steps: simple functions, nonnegative functions, and then general functions.3.3.1 Counting principles Knewton Alta MATH 1340 C1608 2020WI - STATISTICS 3.3.1 Counting principles Counting with combinations Question A manager is scheduling 24 employees for different shifts. If he needs to choose 8 employees for each shift, how many different groups of eight employees can he make without repetition? Provide your answer below:4. Problem 4(15 pt) Let X, Y and Z be independent random variables. X and Y are uniform(0,1) random variables, and Z is uniform(0,2) random variable. Set X1 = X + Z, Y, = 2Y + Z. Find Var(X1 + Yi) and Var(X1 - Yi).Determine whether the value is a discrete random variable, continuous random variable, or not a random variable. a. The weight of a T-bone steak b. The exact time it takes to evaluate 27 + 72 c. The gender of college students d. The distance a baseball travels in the air after being hit e. The number of hits to a website in a day f. The time it takes to fly from City A to City B a. Is the weight of a T-bone steak a discrete random variable, a continuous random variable, or not a random variable? O A. It is a discrete random variable. B. It is a continuous random variable. O C. It is not a random variable b. Is the exact time it takes to evaluate 27 + 72 a discrete random variable, a continuous random variable, or not a random variable? A. It is a continuous random variable. O B. It is a discrete random variable. X C. It is not a random variable c. Is the gender of college students a discrete random variable, a continuous random variable, or not a random variable? X A. It is a continuous random variable. OB. It is a discrete random variable. *C. It is not a random variable d. Is the distance a baseball travels in the air after being hit a discrete random variable, a continuous random variable, or not a random variable? X A. It is a discrete random variable, *B. It is a continuous random variable