pls help me with this question

Problem 4 (35 points): An asset price is modeled by using a sequence of independent and iden- tically distributed continuous random variables X1, X2, . .. with common density function f. We say that a record price occurs at time n if X, > max(X1, X2 . . . , Xn-1). 1. (5 points) Compute P[ a record price occurs at time n]. Justify your answer! Next, consider the variable Y defined as Yi = 0 1 if a record occurs at time i otherwise 2. (5 points) Let Zn be the number of records by time n. Express the variable Zn in terms of the variables Yi. 3. (5 points) Compute E[Y]. 4. (5 points) Give the expected number of records by time n. Hint: do not attempt to calculate the sum. 5. (10 points) Compute var [Yi]. 6. (10 points) Calculate the variance of the number of records by time n. Hint: do not attempt to calculate the sum