How to find probability distribution of $Y=3$X, if Poisson distribution of $X$ has parameter $lambda$?
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Random variable $X$ has Poisson distribution parameter $lambda$. Find the probability distribution of random variable $Y=3X$.
probability-theory probability-distributions random-variables
edited Nov 27 '18 at 14:32
greedoid
40.1k114799
asked Nov 27 '18 at 14:23
No NameNo Name
475
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add a comment |
$begingroup$
Random variable $X$ has Poisson distribution parameter $lambda$. Find the probability distribution of random variable $Y=3X$.
probability-theory probability-distributions random-variables
edited Nov 27 '18 at 14:32
greedoid
40.1k114799
asked Nov 27 '18 at 14:23
No NameNo Name
475
$endgroup$
add a comment |
$begingroup$
Random variable $X$ has Poisson distribution parameter $lambda$. Find the probability distribution of random variable $Y=3X$.
probability-theory probability-distributions random-variables
edited Nov 27 '18 at 14:32
greedoid
40.1k114799
asked Nov 27 '18 at 14:23
No NameNo Name
475
$endgroup$
Random variable $X$ has Poisson distribution parameter $lambda$. Find the probability distribution of random variable $Y=3X$.
probability-theory probability-distributions random-variables
probability-theory probability-distributions random-variables
edited Nov 27 '18 at 14:32
greedoid
40.1k114799
asked Nov 27 '18 at 14:23
No NameNo Name
475
edited Nov 27 '18 at 14:32
greedoid
40.1k114799
asked Nov 27 '18 at 14:23
No NameNo Name
475
edited Nov 27 '18 at 14:32
greedoid
40.1k114799
edited Nov 27 '18 at 14:32
greedoid
40.1k114799
edited Nov 27 '18 at 14:32
greedoid
40.1k114799
40.1k114799
asked Nov 27 '18 at 14:23
No NameNo Name
475
asked Nov 27 '18 at 14:23
No NameNo Name
475
asked Nov 27 '18 at 14:23
No NameNo Name
475
475
add a comment |
add a comment |
1 Answer
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If $3mid k$ then:
$$P(Y=k) = P(3X =k) = P(X={kover 3}) = e^{-lambda}{lambda^{kover 3}over {kover 3}!}$$
else $P(Y=k)=0$.
answered Nov 27 '18 at 14:37
greedoidgreedoid
40.1k114799
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add a comment |
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
If $3mid k$ then:
$$P(Y=k) = P(3X =k) = P(X={kover 3}) = e^{-lambda}{lambda^{kover 3}over {kover 3}!}$$
else $P(Y=k)=0$.
answered Nov 27 '18 at 14:37
greedoidgreedoid
40.1k114799
$endgroup$
add a comment |
$begingroup$
If $3mid k$ then:
$$P(Y=k) = P(3X =k) = P(X={kover 3}) = e^{-lambda}{lambda^{kover 3}over {kover 3}!}$$
else $P(Y=k)=0$.
answered Nov 27 '18 at 14:37
greedoidgreedoid
40.1k114799
$endgroup$
add a comment |
$begingroup$
If $3mid k$ then:
$$P(Y=k) = P(3X =k) = P(X={kover 3}) = e^{-lambda}{lambda^{kover 3}over {kover 3}!}$$
else $P(Y=k)=0$.
answered Nov 27 '18 at 14:37
greedoidgreedoid
40.1k114799
$endgroup$
If $3mid k$ then:
$$P(Y=k) = P(3X =k) = P(X={kover 3}) = e^{-lambda}{lambda^{kover 3}over {kover 3}!}$$
else $P(Y=k)=0$.
answered Nov 27 '18 at 14:37
greedoidgreedoid
40.1k114799
answered Nov 27 '18 at 14:37
greedoidgreedoid
40.1k114799
answered Nov 27 '18 at 14:37
greedoidgreedoid
40.1k114799
answered Nov 27 '18 at 14:37
greedoidgreedoid
40.1k114799
40.1k114799
add a comment |
add a comment |
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