Question at below

a) Find the prob that tomorrow price is grater than 120 TL

b) What can you say about expected value and variance

2. Modeling Asset Returns-The log-normal distribution The log-normal distribution is given by 1 [tax[i132 2 2 for): x0 21:9 a ,x>0 0, elsewhere 2 With Eur) = 90\"" f2} and variance var(X) = 9.02 (es: 1)e2\" Logarithmic asset returns r have been historically modeled as normally distributed such that the related asset prices are modeled by a log-normal distribution. That is, let P, denote today's asset price and, irthennore, let the daily return r be N (u, 02). Then, in a simplified fashion, tomorrow's price is given by P,+1 = Pt - e'\" while the percent change between the two prices, er , is log-normally distributed, that is Ln(u, oz). Consider a very simplied stock price model. Let SD = 100 TL be today's stock price of some company. Model the 1-day dynamic X as S1 = $0 -ex with a normal distribution. You can derive that the ratio of tomorrow's price over today's price is given by :1 = ex follows a log-normal distribution with parameters pi and a. That is, 0 ~LN (p, 52). 50 :1) Find the probability that tomorrow's price is greater than 120 TL. b) What can you say about the expected value and variance of (2D