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S1 Discrete probability distribution

The random variable X has a Poisson distribution with mean 4. The random variable Y is given by

Y = 3X – 7.

(a) Find the mean and variance of Y.
(b) Find the probability that Y is positive.

I have done (a) E(Y) = 5 , Var(Y) = 36

For (b) this is what I got

P(Y > 0)
P( 3X > 7 )
P( X > 7/3 )

but now the mark scheme continues with

P(X ≥ 3)=0.7619 (most likely using tables)

Where did P(X ≥ 3) come from? On some textbooks it says it has something to do with 'discrete probability distribution' but I don't know what this means.

(edited 8 years ago)

Reply 1

M.C. Math

Original post by 10614LW

Hi. In a discrete probability distribution, X can only have integer values.So P(X > 7/3) = P(X > 2 1/3), so the first integer will be 3, hence P(X ≥ 3).