using java- simple code

1. In a town, each day is either sunny or rainy. A sunny day is followed by another sunny day with probability 0.7, whereas a rainy day is followed by a sunny day with probability 0.4. It rains on Monday. (a) Simulate a Markov chain of 100 days for the weather: First simulate the weather on Tuesday (based on Monday's weather), and then simulate the weather on Wednesday (based on Tuesday's weather), etc. Write down the weather of the 100 days. [Hint: To generate a random number X that takes value 1 with probability 0.7 and 2 otherwise, first generate a uniform random variable U on [0, 1], and then let X if U 0.7 and X2 otherwise.] (b) Repeat (a) but for 10000 days. What proportions of sunny and rainy days do you have? Compare the result to the stationary distribution (which was derived in the lecture)