
#1




Help Needed with these Problems
I am stuck on how to solve these problems. If someone can help me, that would be greatly appreciated.
1) Suppose that X and Y are independent continuous random variables with density functions fX and fY . Let T = min(X, Y ) and V = max(X, Y ). Find the marginal density functions fT of T and fV of V. I know that I should find the CDF of T and V and differentiate those to give me my marginal density functions, but how do I calculate the CDF of T and V? 2) Let 0 < p < 1 and 0 < r < 1 with p not being equal to r. You repeat a trial with success probability p until you see the first success. I repeat a trial with success probability r until I see the first success. All the trials are independent of each other. a)What is the probability that you and I performed the same number of trials? b) Let Z be the total number of trials you and I performed altogether. Find the possible values and the probability mass function of Z. 3) Let X and Y be independent exponential random variables with parameter 1. (a) Calculate the probability P(Y ≥ X ≥ 2). (b) Find the density function of the random variable X − Y . Sorry for this long post, but hopefully someone can help me with these problems. 
#3




These look too hard for exam P. Where did you find them?
I will do #2 for you. Let X be the number of trials until first success (w/ success probability p) Let Y be the number of trials until first success (w/ success probability r) (a) (b) Let be an integer. unless I made a mistake somewhere... (PMF is 0 if z is not an integer >=2) 
#4




3a is just a double integral. Draw a picture. For 3b. here is a more general case:
http://www.math.wm.edu/~leemis/chart...ialLaplace.pdf 
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