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

b

step-by-step explanation:

the answer is; biodiversity resulting from few ancestors

adaptive radiation occurs when a population is subjected to a large natural environment with spatial ecological variations. the parts of the population in the different ecologies begin to adapt to their local environments. due to non-random mating across the large populations, this causes the different populations from the large population to speciate within their local environments. they, therefore, diverge to different species sharing a common ancestor.