# Thread: the probability distribution of Y

1. ## the probability distribution of Y

Let $m(t) = 0.21+ 0.12e^{2t} + 0.38e^{4t} + 0.29e^{6t}$ for some discrete random variable Y. Use m(t) to find each
of the following.
(A) E(Y)
(B) V(Y)
(C) The probability distribution of Y.
I have found E(Y)=3.5, and V(Y)=4.75, what is the probability distribution of Y, looks like a binimoinal, but not exactly a binimoial

2. ## Re: the probability distribution of Y

Originally Posted by wopashui
Let $m(t) = 0.21+ 0.12e^{2t} + 0.38e^{4t} + 0.29e^{6t}$ for some discrete random variable Y. Use m(t) to find each
of the following.
(A) E(Y)
(B) V(Y)
(C) The probability distribution of Y.
I have found E(Y)=3.5, and V(Y)=4.75, what is the probability distribution of Y, looks like a binimoinal, but not exactly a binimoial
X can take on the values 0, 2, 4, 6 with non-zero probability.

Pr(X = 0) = 0.21, Pr(X = 2) = 0.12, Pr(X = 4) = ...., Pr(X = 6) = ....

Look at the definition of the mgf for a discrete distribution.

3. ## Re: the probability distribution of Y

Originally Posted by mr fantastic
X can take on the values 0, 2, 4, 6 with non-zero probability.

Pr(X = 0) = 0.21, Pr(X = 2) = 0.12, Pr(X = 4) = ...., Pr(X = 6) = ....

Look at the definition of the mgf for a discrete distribution.
I still don't understanf the pattern, why is it like that, x=o means t=0?

4. ## Re: the probability distribution of Y

Originally Posted by wopashui
I still don't understanf the pattern, why is it like that, x=o means t=0?
Originally Posted by Mr Fantastic
[snip] Look at the definition of the mgf for a discrete distribution.
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