3. (Weather prediction revisit) Assume a day is either sunny or rainy, and the weather condition is only depending on the preceding day. A sunny day is 90% likely to be followed by another sunny day, and a rainy day is 50% likely to be followed by another rainy day. Given that it is 75% likely to be rain today, 09 05 a) find the eigendecomposition of transition matrix P = ( 1 o 5) =VAV~L b) what is the probability of rainy in 10 days? ) what is the probability of rainy in 100 days? d) whatis the probability of rainy in a long run? (Hint: compute ,!im P"Fy, where Fy = (0.25,0.75)7.)