Question:

Please help keep getting it wrong!

According to the WHO MONICA Project the mean blood pressure for people in China is 128 mmHg with a standard deviation of 23 mmHg. Assume that blood pressure is normally distributed.

Round the probabilities to four decimal places.

b) Find the probability that a randomly selected person in China has a blood pressure of 110.9 mmHg or more.

c) Find the probability that a randomly selected person in China has a blood pressure of 152.3 mmHg or less.

d) Find the probability that a randomly selected person in China has a blood pressure between 110.9 and 152.3 mmHg.

e) Find the probability that randomly selected person in China has a blood pressure that is at most 70.5 mmHg.

7. (Bonus) a. Sketch the state-transition diagram for the Markov chain with the following transition probability matrix: (1.5 points) 0.5 0.5 0 1.0 0 0 0 P = 0.5 0 0.25 0.25 0 0.25 0.25 0.5 b. Find the transition probability matrix for the Markov chain shown. (1.5 points) 0.5 3 0.5QUESTION 1 Consider a Markov chain with (one-step) transition probability matrix P= How many communicating classes does the Markov chain have? QUESTION 2 Consider a Markov chain with (one-step) transition probability matrix P= " . How many communicating classes does the Markov chain have? QUESTION 3 Consider a Markov chain with (one-step) transition probability matrix P=|9 . What is the period of state 0? (If the state is aperiodic, enter 1.)9. Suppose that a Markov chain has transition probability matrix 0 50 .50 0 P = .50 .25 .25 2 0 .50 .50 Give the values of limn-+x P(X, = i ) for i = 0, 1, 2. 10. Suppose that a Markov chain has transition probability matrix 0 1 2 .50 40 .10 P = .10 .50 .40 2 .40 .10 .50 Find the stationary probabilities To, 71, 12.2. Spectral Versus Singular Value Decomposition: Consider a linear operator A with matrix representation 1 3 A _ [7 _1] (a) Compute the spectral decomposition and singular 1mlue decomposition of A. (1:) Sketch ANSI}, the image of the unit circle under .A. (c) Compare your answers to parts (a) and {b} and draw a conclusion