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by EdisonCruise
October 11th, 2013, 1:47 am
Forum: Student Forum
Topic: How to interpret the expectation and variance in this case?
Replies: 1
Views: 5747

How to interpret the expectation and variance in this case?

The default probability p of bond A is 0.5. Let X be the indicator for the event that bond A defaults. Then the expectation of X is 0.5, and variance of X is p(1-p)=0.25.I cannot understand what the meaning of expectation of X is. Also how can we calculate the variance of X in that way?
by EdisonCruise
September 24th, 2013, 2:45 am
Forum: Brainteaser Forum
Topic: Can we solve the problem by maringale?
Replies: 5
Views: 7156

Can we solve the problem by maringale?

<t>A gambler starts with an initial fortune of i dollars. On each successive game, the gambler wins $1 with probability p, 0<p<1, or loss $1 with probability q=1-p. He will stop if he either accumulates N dollars or loses all his money. What is the probability that he will end up with N dollars?Assu...
by EdisonCruise
September 15th, 2013, 1:36 am
Forum: Brainteaser Forum
Topic: The Dart game problem
Replies: 3
Views: 8216

The Dart game problem

<t>Jason throws two darts at a dartboard, aiming for the center. The second dart lands farther from the center than the first. If Jason throws a third dart aiming for the center, what is the probability that the third throw is farther from the center than the first? Assume Jason's skillfulness is co...
by EdisonCruise
September 7th, 2013, 1:11 am
Forum: Brainteaser Forum
Topic: What's the expected return of this game?
Replies: 3
Views: 7710

What's the expected return of this game?

<t>Thank you Vanubis1. I think it makes sense.I also wonder if there is any quick way to solve E(n)=(3+4+5+6)/6-n*4/6+2/6*E(n+1)?What I can think is let E(n)=an+b. Then we have2a*n+2b=a+9-2nLet n= 1,2we can solve a = -1 and b =4.Finally check if E(n)=4-n a solution. In this way, I am not sure if the...
by EdisonCruise
September 6th, 2013, 1:22 am
Forum: Brainteaser Forum
Topic: What's the expected return of this game?
Replies: 3
Views: 7710

What's the expected return of this game?

<t>There is a dice with number from 1 to 6. You pay 1 dollar to roll the dice each time and you get the return as the dice number. What's your expected return?I try to solve it in this way. I list the return (gained-paid) in each round against the dice number below: dice number 1 2 3 4 5 6return rou...
by EdisonCruise
August 1st, 2013, 4:14 am
Forum: Brainteaser Forum
Topic: tie ropes to form a ring
Replies: 10
Views: 9333

tie ropes to form a ring

there are 100 ropes ? if you tie 100 ends together, what would be the expected number of ropes that would have tied to their own end and be in a ring?
by EdisonCruise
August 1st, 2013, 4:10 am
Forum: Student Forum
Topic: How to calculate conditional expectation?
Replies: 0
Views: 6512

How to calculate conditional expectation?

Assume X and Y are independent variable, f(x) and g(y) are their probability density functions. Can the conditional expectation E{X=x|X+Y<3} be calculated as below?
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