You created a random number generator that works as follows: With probability p it selects a number X from the standard normal distribution N(0,1), and with complimentary probability (1-p) it selects a random number X from an off-central normal distribution N(5, 1). Write the distribution function of X. How would you attempt this. Obviously the variance increases. and the mean is a weighted average of the two. but as far as getting fx(x) I am stumped. Is it correct to add the two distributions together and simplify? (p)*N(0,1) + (1-p)*N(5,1) using the gaussian equation?