Let x and y be independent continuous random variables that are uniformly distributed on (0,1). let h=(x+2)y. find the probability p(lnh≥z) where z is a given number that satisfies ez< 2. your answer should be a function of z. hint: condition on x. p(lnh≥z1)= ? let x be a standard normal random variable, and let fx(x) be its cdf. consider the random variable z=fx(x). find the pdf fz(z) of z. note that fz(z) takes values in (0,1) .fz(z)= ?

Looks like there are two distinct problems here.

Conditioning on involves interpreting this probability for all possible fixed values of :

We have , and over this domain . Since is fixed, we can omit the conditioning notation to leave us with

has CDF

Then we can write our integral as

Using the method of distribution functions, we have

33

step-by-step explanation: g=6

typically if you want , you would actually put questions here for us to you. but hey, that's just me. maybe someone will magically answer the questions for you without knowing what they are.