Q$4.$ Delta and Gamma with Uniform Distribution $(20$ points$)$

Current underlying price at $1000,$ and you expect price at expiration follows uniform distribution

with mean absolute deviation of $200.$

You LONG $100$ PUTs with strike at $900.$

Q$4$a$.$ What is the TOTAL delta of your $100$ LONG PUTs position? $(2$ points$)$

Q$4$b$.$ How many shares do you need in order to offset the option delta from Q$4$a$?$ Do you long or

short the underlying stock $(2$ points$)?$

Q $4$ c $.$ What is the total gamma value of your hedged option positions from Q $4$ a and Q $4$ b $?(2$ points$)$

Q$4$d$.$ For the hedged option position $($LONG PUTs, hedged with shares$),$ what is the PnL from

$($starting$)$ delta, and from gamma respectively, when underlying moves from $1000$ to $950?(3$

points$)$