Recent content by uva123

Homework Statement Prove if {bn} converges to B and B ≠ 0 and bn ≠ 0 for all n, then there is M>0 such that |bn|≥M for for all n. Homework Equations What I have so far: I know that if {bn} converges to B and B ≠ 0 then their is a positive real number M and a positive integer N such...

Homework Statement suppose {an} and {bn} are sequences such that {an} converges to A where A does not equal zero and {(an)(bn)} converges. prove that {bn} converges. Homework Equations What i have so far: (Note:let E be epsilon) i know that if {an} converges to A and {bn}converges...

im really not sure.

Homework Statement Suppose that the radius X of a circle is a random variable having the following p.d.f.: f(x)={ (1/8)(3x=1) for 0<x<2 0 otherwise Determine the p.d.f. of the area of the circle and the circumference of the circle. Homework Equations...

Homework Statement Suppose that a fair coin is tossed repeatedly until a head is obtained for the first time. (a) What is the expected number of tosses that will be required? (b) What is the expected number of tails that will be obtained before the first head is obtained? Homework...

Homework Statement Suppose that a particle starts at the origin of the real line and moves along the line in jumps of one unit. For each jump, the probability is p that the particle will jump one unit to the left and the probability is (1-p) that the particle will jump one unit to the...

Homework Statement Suppose that a point is chosen at random on a stick that has length 15 inches, and that the stick is broken into two pieces at that point. Find the expected value of the lengths of the two pieces. Homework Equations E(x)=\sumf(x)xdx from -infinity to +infinity...

Homework Statement Suppose that X1,...,Xn form a random sample from a inform distribution on the interval [0,1] and that the random variable Ynmax{X1,...,Xn}. Determine the smallest value of n such that Pr[Yn≥.99]≥.95 Homework Equations W=Yn-Y1 where W is the range of the sample...