Chapter 2: Problem 6
Let \(X\) and \(Y\) have the joint pdf \(f(x, y)=1,-x
Chapter 2: Problem 6
Let \(X\) and \(Y\) have the joint pdf \(f(x, y)=1,-x
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Get started for freeFive cards are drawn at random and without replacement from an ordinary deck of cards. Let \(X_{1}\) and \(X_{2}\) denote, respectively, the number of spades and the number of hearts that appear in the five cards. (a) Determine the joint pmf of \(X_{1}\) and \(X_{2}\). (b) Find the two marginal pmfs. (c) What is the conditional pmf of \(X_{2}\), given \(X_{1}=x_{1} ?\)
Let \(X_{1}, X_{2}, X_{3}\), and \(X_{4}\) be four independent random variables,
each with pdf \(f(x)=3(1-x)^{2}, 0
Suppose that a man leaves for work between 8:00 A.M.and 8:30 A.M. and takes between 40 and 50 minutes to get to the office. Let \(X\) denote the time of departure and let \(Y\) denote the time of travel. If we assume that these random variables are independent and uniformly distributed, find the probability that he arrives at the office before \(9: 00\) A.M..
Let \(X\) and \(Y\) have the joint pdf \(f(x, y)=2 \exp \\{-(x+y)\\},
0
Let \(X_{1}\) and \(X_{2}\) have the joint pmf \(p\left(x_{1}, x_{2}\right)=x_{1} x_{2} / 36, x_{1}=1,2,3\) and \(x_{2}=1,2,3\), zero elsewhere. Find first the joint pmf of \(Y_{1}=X_{1} X_{2}\) and \(Y_{2}=X_{2}\) and then find the marginal pmf of \(Y_{1}\).
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