Question: For X ~ Geo(p) having a geometric distribution such that P(X = x) = (1-p)'p,x=1, 2,... (i) Show that _, P ( X = x

For X ~ Geo(p) having a geometric distribution such that P(X = x) = (1-p)"'p,x=1, 2,... (i) Show that _, P ( X = x ) = 1 . (5 marks) (ii) Derive the moment generating function Mx (t) . (5 marks) (iii) Therefore show that E(X) =- if q=1-p. (5 marks) p (iv) The random variable X represents the year in which a motor vehicle driver experiences the first accident since driving in a new city of residence. 3*-1 P ( X = x) = 4 X Find the year in which this driver is expected to have the first accident

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