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Simple S1 question that i need help on watch

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1. The Random variable X has the following probability distribution:

x: 1 5 9
P(X=x): a b c

where a, b and c are constants. It is known tht P(X < 4) = P(X > 4) and P(X =< 5) = 2P (X > 5)

a) Find the values of a, b and c
b) Find F(8)

***a detailed, logical answer would be much appreciated***
2. (Original post by h_cube3000)
The Random variable X has the following probability distribution:

x: 1 5 9
P(X=x): a b c

where a, b and c are constants. It is known tht P(X < 4) = P(X > 4) and P(X =< 5) = 2P (X > 5)

a) Find the values of a, b and c
b) Find F(8)

***a detailed, logical answer would be much appreciated***
P(X < 4) = P(X > 4) => a = b+c
P(X =< 5) = 2P (X > 5) => a+b = 2c
ΣP(X==x) = 1 => a+b+c = 1

solving simultaneously:

a=1/2
b=1/6
c=1/3

b) F(8) = P(X<8) = P(X=1) + P(X=5) = 1/2 + 1/3 = 2/3

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