- October 17th, 2013, 7:32 pm
- Forum: Student Forum
- Topic: How to interpret the probability in the figure?
- Replies:
**12** - Views:
**6383**

<t>Thank you for your responses. I still hope to understand this type of problem further. Now suppose Y=min(X1, X2). One can get P{Y>=y}=(1-y)^2. From the attached figure, it can be shown that P{Y>=y and Z<=z} = (z-y)^2. However, can we calculate P{Y>=y and Z<=z} mathematically without the help of f...

- October 16th, 2013, 1:27 am
- Forum: Student Forum
- Topic: How to interpret the probability in the figure?
- Replies:
**12** - Views:
**6383**

<t>Let X1 and X2 be IID random variables with uniform distribution between 0 and 1. z = max(X1, X2).I can calculate the cdf of P{Z<=z}=z^2 analytically. But how to interpret this formula from the attached figure? why the square (0,0)_(z,0)_(z,z)_(0,z) is P{Z<=z}?Thank you. Thank you for your suggest...

- October 11th, 2013, 1:47 am
- Forum: Student Forum
- Topic: How to interpret the expectation and variance in this case?
- Replies:
**1** - Views:
**5753**

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?

- September 24th, 2013, 2:45 am
- Forum: Brainteaser Forum
- Topic: Can we solve the problem by maringale?
- Replies:
**5** - Views:
**7187**

<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...

- September 15th, 2013, 1:36 am
- Forum: Brainteaser Forum
- Topic: The Dart game problem
- Replies:
**3** - Views:
**8225**

<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...

- September 7th, 2013, 1:11 am
- Forum: Brainteaser Forum
- Topic: What's the expected return of this game?
- Replies:
**3** - Views:
**7718**

<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...

- September 6th, 2013, 1:22 am
- Forum: Brainteaser Forum
- Topic: What's the expected return of this game?
- Replies:
**3** - Views:
**7718**

<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...

- August 1st, 2013, 4:14 am
- Forum: Brainteaser Forum
- Topic: tie ropes to form a ring
- Replies:
**10** - Views:
**9368**

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?

- August 1st, 2013, 4:10 am
- Forum: Student Forum
- Topic: How to calculate conditional expectation?
- Replies:
**0** - Views:
**6520**

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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