# Probability

1. Let X be a random variable with Sx = {0, 1, 2, .. .} and probability mass func-tion of the formPx ( k) = c2k.(a) Determine c.[ Px (k) = 1KE SxSum of geometric series> E PX CK ) = [ C2-k= a& first termKECratio between temCE 2**C [ 1 + 3 + 72+ 23+ .a =l , r= 2E PX (K ) = 1=C(T- I )KESX20 = 1= C (X )= 2C .” .. Px ( k ) = = ( 2)*.(b) Is X more likely to take values that are divisible by 4, or values that arenot divisible by 4? Justify your answer.

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By computing the Probability of value divisible by 4 & not divisible byDivisible by 4 :Not divisible by 4 :4.SX = 10, 4, 8, 12 …. .P( Not divisible by 4)[ PX (K) = [ + (2)- KXGSxK= 0= 1 – P(divisible by 4 )*= [( ) + (# ) + (= )8+…]=. = [ItCAN ” + ( # ) 8 +..] <75. Hence, X ismore likely to take: 3 (5/16) =75values that aredivisible by 4 .

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