# propability when Y = ln(X) [closed]

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 $$X$$)

• Probability cannot equal 5. – Dave Jun 5 at 17:40
• Oh I have written the wrong number by mistake – Anonym Jun 5 at 17:41
• I will edit it now – Anonym Jun 5 at 17:41
• 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) ? – doubled Jun 5 at 17:49
• 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. – Peter Flom Jun 7 at 11:51

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.