I am unable to solve this question in my past-year paper.
.Let $A$ be pdf and $B$ be cdf, of the standard normal variable $Z$. Let $X = 4Z-1$
The question given was to find the median of $X$
No additional information was given, like intervals $(a,b)$ as I am aware that pdf (probability density function) and cdf (cumulative distribution function) require these intervals.
I have tried the formula $\frac{1}{\sqrt{2πσ}}\exp(\frac{-1}{2})(\frac{Y-μ}{σ})^2$ to obtain pdf and subbing $(0.5, -\infty=0)$ into pdf to obtain cdf, ultimately getting to this equation
$e^{-x^2/2}$ = 2.25
But was unable to continue after applying $\ln$ to both sides, since I cannot square root a negative number.
Can someone please explain how to solve this?
A standard normal distribution has $N(0,1)$ as its distribution. $X$ has distribution $(4 \times 0-1,4 \times 1)= (-1,4)$. Since the distribution is symmetrical the mean is equal to the median. Thus the median is -1