Problem 3
Let \(X\) have the pdf \(f(x)=(x+2) / 18,-2
Problem 3
List all possible arrangements of the four letters \(m, a, r\), and \(y .\) Let \(C_{1}\) be the collection of the arrangements in which \(y\) is in the last position. Let \(C_{2}\) be the collection of the arrangements in which \(m\) is in the first position. Find the union and the intersection of \(C_{1}\) and \(C_{2}\).
Problem 3
Let \(p_{X}(x)=x / 15, x=1,2,3,4,5\), zero elsewhere, be the pmf of \(X\). Find
\(P(X=1\) or 2\(), P\left(\frac{1}{2}
Problem 3
Let the subsets \(C_{1}=\left\\{\frac{1}{4}
Problem 3
If \(X\) is a random variable such that \(E(X)=3\) and \(E\left(X^{2}\right)=13\), use Chebyshev's inequality to determine a lower bound for the probability \(P(-2<\) \(X<8)\)
Problem 3
For each of the following distributions, compute \(P(\mu-2 \sigma
Problem 4
Cast a die two independent times and let \(X\) equal the absolute value of the difference of the two resulting values (the numbers on the up sides). Find the pmf of \(X\). Hint: It is not necessary to find a formula for the pmf.
Problem 4
Concerning DeMorgan's Laws \((1.2 .6)\) and \((1.2 .7)\) : (a) Use Venn diagrams to verify the laws. (b) Show that the laws are true. (c) Generalize the laws to countable unions and intersections.
Problem 4
From a well-shuffled deck of ordinary playing cards, four cards are turned over one at a time without replacement. What is the probability that the spades and red cards alternate?
Problem 4
If the variance of the random variable \(X\) exists, show that $$ E\left(X^{2}\right) \geq[E(X)]^{2} $$
