Stats/Math Problems and Riddles #2

iaafr · June 22, 2019, 1:34am

big_ass · June 22, 2019, 2:11am

Here is my answer to the other question

big_ass · June 22, 2019, 2:18am

Expected number: sum(totalchildren*probability)

Gender ratio:

1/(sum(totalchildren-1*probability))

KrazyKat · June 22, 2019, 2:50am

64 couples.

First birth. 32 girls, 32 boys. 32-32
Second birth. 16 girls, 16 boys. 48-48
Third birth. 8 girls, 8 boys. 56-56
Fourth birth. 4 girls, 4 boys. 60-60
Fifth birth. 2 girls, 2 boys. 62-62
Sixth birth. 1 girl, 1 boy. 63-63

It's always the same. Similar to Zeno's paradox.

iaafr · June 22, 2019, 3:04am

i guess that makes the expected number of children / couple 2

KrazyKat · June 22, 2019, 3:50am

The results may vary. In India, they test for gender, and abort the girls, because of the dowry.

ironstove · June 22, 2019, 7:30am

Here are the rest of the problems for those that are curious:

github.com

kojino/120-Data-Science-Interview-Questions/blob/master/probability.md

## Probability (19 questions)


#### 1. Bobo the amoeba has a 25%, 25%, and 50% chance of producing 0, 1, or 2 o spring, respectively. Each of Bobo’s descendants also have the same probabilities. What is the probability that Bobo’s lineage dies out?
  - p=1/4+1/4*p+1/2*p^2 => p=1/2
#### 2. In any 15-minute interval, there is a 20% probability that you will see at least one shooting star. What is the proba- bility that you see at least one shooting star in the period of an hour?
  - 1-(0.8)^4. Or, we can use Poisson processes
#### 3. How can you generate a random number between 1 - 7 with only a die?
* Launch it 3 times: each throw sets the nth bit of the result. 
* For each launch, if the value is 1-3, record a 0, else 1.
The result is between 0 (000) and 7 (111), evenly spread (3 independent throw). Repeat the throws if 0 was obtained: the process stops on evenly spread values.
#### 4. How can you get a fair coin toss if someone hands you a coin that is weighted to come up heads more often than tails?
  - Flip twice and if HT then H, TH then T.
#### 5. You have an 50-50 mixture of two normal distributions with the same standard deviation. How far apart do the means need to be in order for this distribution to be bimodal?
  - more than two standard deviations
#### 6. Given draws from a normal distribution with known parameters, how can you simulate draws from a uniform distribution?
  - plug in the value to the CDF of the same random variable
#### 7. A certain couple tells you that they have two children, at least one of which is a girl. What is the probability that they have two girls?
  - 1/3
#### 8. You have a group of couples that decide to have children until they have their first girl, after which they stop having children. What is the expected gender ratio of the children that are born? What is the expected number of children each couple will have?

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a2pas · June 22, 2019, 4:02pm

wow yeah I hATE probability and statistics

girlpool · June 22, 2019, 5:07pm

a2pas · June 22, 2019, 5:57pm

8X82dSg

jones · June 25, 2019, 1:23am

sum two die rolls, mask to 3 bits. reroll on 000.

jones · June 25, 2019, 1:28am

take the first bit of stream_cipher(random_key, coin_flips).

jones · June 25, 2019, 1:29am

33%

jones · June 25, 2019, 1:31am

i don't know how to do four off the top fo my head.

Friend · June 25, 2019, 1:39am

i kinda missed the ship on this but this throws me back to stats class <3 i miss math

anon31000304 · June 25, 2019, 1:40am

the last math class i took was algebra 2 and i got a 61% (pass). i'm SO bad at math

Friend · June 25, 2019, 1:40am

anyways im sure the meme answer to #3 is

implying theres a gender binary

anon31000304 · June 25, 2019, 1:40am

just kidding i took one in junior college and failed that

Friend · June 25, 2019, 1:41am

@ironstove do we know the distribution of heads to tails for the weighted coin or is it arbitrary?

jones · June 25, 2019, 1:42am

generate source of randomness -> xor it with weigthed coin outcome.