Finding the probability generating function of $Z= mY + n$ where $Y$ is random variable and $m,n$ are...
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Let $G_Y(s)$ be the probability generating function of $Y$.
The probability generating function of $Z$ is defined as:
$$G_z(s) = E(s^Z)$$
$$= E(s^{mY + n})$$
$$= E(s^{mY}s^n)$$
$$= s^{n} E((s^{m})^Y)$$
$$= s^{n} [E(s^Y)]^m$$
$$= s^n [G_Y(s)]^m$$
Is this the right approach?
Thanks!
probability probability-distributions generating-functions
asked Nov 16 at 13:24
Sul
313114
add a comment |
up vote
0
down vote
favorite
Let $G_Y(s)$ be the probability generating function of $Y$.
The probability generating function of $Z$ is defined as:
$$G_z(s) = E(s^Z)$$
$$= E(s^{mY + n})$$
$$= E(s^{mY}s^n)$$
$$= s^{n} E((s^{m})^Y)$$
$$= s^{n} [E(s^Y)]^m$$
$$= s^n [G_Y(s)]^m$$
Is this the right approach?
Thanks!
probability probability-distributions generating-functions
asked Nov 16 at 13:24
Sul
313114
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Let $G_Y(s)$ be the probability generating function of $Y$.
The probability generating function of $Z$ is defined as:
$$G_z(s) = E(s^Z)$$
$$= E(s^{mY + n})$$
$$= E(s^{mY}s^n)$$
$$= s^{n} E((s^{m})^Y)$$
$$= s^{n} [E(s^Y)]^m$$
$$= s^n [G_Y(s)]^m$$
Is this the right approach?
Thanks!
probability probability-distributions generating-functions
asked Nov 16 at 13:24
Sul
313114
Let $G_Y(s)$ be the probability generating function of $Y$.
The probability generating function of $Z$ is defined as:
$$G_z(s) = E(s^Z)$$
$$= E(s^{mY + n})$$
$$= E(s^{mY}s^n)$$
$$= s^{n} E((s^{m})^Y)$$
$$= s^{n} [E(s^Y)]^m$$
$$= s^n [G_Y(s)]^m$$
Is this the right approach?
Thanks!
probability probability-distributions generating-functions
probability probability-distributions generating-functions
asked Nov 16 at 13:24
Sul
313114
asked Nov 16 at 13:24
Sul
313114
asked Nov 16 at 13:24
Sul
313114
asked Nov 16 at 13:24
Sul
313114
asked Nov 16 at 13:24
Sul
313114
313114
add a comment |
add a comment |
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