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# S1 Geometric distributions help watch

1. I have a question:
The random variable T can take values 1, 2, 3,...) and has a geometric distribution. It is given that P(T= 1 or 2) = 0.4375. Find the value of P(T=1).
I don't know how to approach this, but the answer is 0.25
2. let P( T= 1) = a

then P ( T = 2 ) = ar

P ( T = 3 ) = ar2 etc

we know that the total of the infinite probabilities is 1...

the sum to infinity of a G.P is a / ( 1 - r )

so a / ( 1 - r ) = 1

we are told that P( T = 1 ) + P( T = 2 ) = 0.4375

so a + ar = 0.4375... now combine this with a / ( 1 - r ) = 1 to find a

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