Statistics S1 OCR AS LEVELWatch
(i) (a) Find the probability that X = 10.
(b) Find the probability that X < 10.
(ii) Find the expected number of steps taken by the token.
(iii) Hence, write down the value of E( X ).
I dont understand the question or how to work out any of the solutions please can somebody help me ? !
I especially dont understand part b)
I'm going to quote in Puddles the Monkey now so she can move your thread to the right place if it's needed.
ia. i would expect this to be 0.8^10 or smth? because it must move in the x-direction 10 times before it moves in the y-direction, so I would expect something reminiscent of a geometric distribution with Geo(0.8) idk?
b. unsure, but it would mean that the counter had moved in the y-direction before 10 moves in the x-direction had occurred, the only way i could process this is to add all of x=0,1,2,3,4,5,6,7,8,9 together, idk if that'd take too long it'd be like- (0.2)+(0.2x0.8)+(0.2x0.8^2)... etc until (0.2x0.8^9) i think idk
ii. expected number of steps i would guess would just be 8? because you have an 8/10 chance of going in the x-direction until you are expected to roll a y and stop.
iii. idk sorry its a weird af question
please dont take this as the answer this is just guesswork, is there a mark scheme hidden anywhere? would be good if we could read it and see the real answers
bi) What buckey suggested, or use sum to n of a geometric series with a= 0.2, r= 0.8, n=10. (=0.8926)
bii) We stop when we get a y. This assuredly will happen after 0.2^-1 = 5 attempts.
biii) We land on 0.2 on the fifth go so this is the final step. Therefore beforehand we covered 4 X units, so = 4.
These could be wrong.