let Y be a random vairable giving the no. of heads minus the no. of tails in 2 tosses of a coin. assuming that the coin is biased sot aht the head is twice as likely to occur as the tail,

calculate the mean and standard deviation.

then calculate the cumulative distribution function.

i just learnt this chapter and am completely lost. can someone help me?

these are my working:

P(-1) = 6/27 where there are 2 tails and 1 head

P (1) = 18/27 where there are 2 heads and one tail

P(-3) = 1/27 where there are 3 tails

P( 3) 8/27 wherer there are 3 heads

thus the mean = 1.2222 and the standard deviation = 1.547

how do i go about doing the last part? i know that to find the cumulative distribution function, i have to find the area under p(y) but i do not have an equation to integrate.

did i do something wrong or is there another method to solve this?

thank you!