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If $Y = \ln(X)$ and $P(Y) = 0.55$

Can i say that $P(X) = e^{P(Y)} = e^{0.55}$ ?

($P(Y)$ is the probability of $Y$, and $P(X)$ is the probability of $X$)

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    $\begingroup$ Probability cannot equal 5. $\endgroup$ – Dave Jun 5 at 17:40
  • $\begingroup$ Oh I have written the wrong number by mistake $\endgroup$ – Anonym Jun 5 at 17:41
  • $\begingroup$ I will edit it now $\endgroup$ – Anonym Jun 5 at 17:41
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    $\begingroup$ What is P(Y), and what is Y? If Y is the event "having 10 apples", what does ln("having 10 apples") mean? Or maybe Y is a random variable and you mean P(Y = a) or P(Y < a) ? $\endgroup$ – doubled Jun 5 at 17:49
  • $\begingroup$ Probability of Y being what? And X being what? When you take the log of something, it implies that that something is numeric; but P(Y) = 0.55 only makes sense by itself if Y is some dichotomy. $\endgroup$ – Peter Flom Jun 7 at 11:51
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First of all, your notation needs revision. Let's call $X,Y$ as random variables with the relation $\log X=Y$. Since $P(Y)$ doesn't make sense, it should be something like $P(Y=y)=0.55$, i.e. probability of the RV $Y$ being equal to a specific value, namely $y$, is $0.55$. Following similarly, if you look for $P(X=x)$, for a specific value $x$ and we have the same relation between between these specific values, i.e. $\log x = y$, then $$P(X=x)=P(e^Y=x)=P(Y=\log x)=P(Y=y)=0.55$$

And, $P(X) = e^{P(Y)} = e^{0.55}$ would never make sense because it's greater than $1$.

Some more notes on your notation, i.e. why don't $P(X),P(Y)$ make sense? The notation $P(.)$ denotes the probability of an event. For example, $Y=y$ is an event, i.e. the event that $Y$ is equal to some specific number $y$. But, on its own $Y$ is not an event and $P(Y)$ doesn't make sense.

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    $\begingroup$ Just a thought: it seems like OP may not fully understand probabilities yet, so may be worth adding a sentence or two in your answer to explain why P(Y) doesn't make sense so that when they read your answer, they follow from start to end. $\endgroup$ – doubled Jun 5 at 17:55
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    $\begingroup$ @doubled Taken your suggestion. $\endgroup$ – gunes Jun 5 at 18:00

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