Paste R variable values into Latex Expression in R Legend (Rmd)

The goal is to get the R variable values into the legend of the plot, while also rendering "mu" and "sigma" in true latex. I can get either the R values into the legend, or the latex to render correctly, but not both at the same time, and all other posts I found so far only wanted to do one or the other (e.g. using expression(mu) and cat(). I am working in an Rmd document, so Latex packages used in other solutions are not straightforward to employ here.

Here a working example:

p <- seq(0, 1, 0.001)
h_p <- asin(sqrt(p))

mle_mu <- mean(h_p)
mle_sigma <- sd(h_p)

digits <- 3
plot(ecdf(h_p), main = 'Cumulative Distribution Function',
     xlab = 'Value', ylab = 'CDF')

x_values <- seq(-3, 3, length.out = 1000)
cdf_values <- pnorm(x_values, mean = mle_mu, sd = mle_sigma)
lines(x_values, cdf_values, col = 'blue', type = "l")

legend('bottomright', 
       legend = c('ECDF of h(p)', 
                  paste('Normal CDF, MLE mean =', round(mle_mu, digits), 
                        ', MLE sd =', round(mle_sigma, digits), sep = '')), 
       col = c('black', 'blue'), 
       lty = 1)

You can use bquote to quote its argument except that terms wrapped in .() are evaluated in the specified environment (default: parent.frame(), i.e. R_GlobalEnv).

In bquote, use paste() to juxtapose plain texts and mathematical annotations. For more details, see ?plotmath.

legend('bottomright', 
       legend = c("ECDF of h(p)",
                  bquote(paste("Normal CDF, MLE ", mu == .(round(mle_mu, digits)),
                               ", MLE ", sigma == .(round(mle_sigma, digits))))), 
       col = c('black', 'blue'), 
       lty = 1)