3 issues I cannot solve

[1211212]

1) Person X buys 10 stocks of Y at 66€/stock price. X estimates that the stock Y has 60% chance to rise 10%, and 40% chance to decrease 10%. What is the probability of at least X breaking even if X cashes out after 4 years. I don't know how to arrive since can't use normal binomial distribution due to having the "at least part" (3 OR 4 years of positive growth). Tried to go the other way around, since 3 losses means not breaking even but 1-nCr(4,3)*0.4^3 *0.6 does not yield the correct answer.

2) < Link to "Most Viral Images" at imgur removed >. Honestly I don't have a clue as to how to calculate this.

3) In hockey penalties have 30% chance of happening. If in penalties where each team do 3 penalties one goalie keeps a clear sheet but the other doesn't? So clear sheet is 0.7^3 but how to proceed from there (chance of at least 1 goal)? Thought about 0.7^3 *(1-0.7^3) but that's not correct.



These are old entrance exam questions and I'm practicing maths portion but its been quite a while since I was in gymnasium and needed these specific calculations so if someone can show me how to calculate these it would help me immensely as to understand the maths behind them.

 

[HallsofIvy]

1) Person X buys 10 stocks of Y at 66€/stock price. X estimates that the stock Y has 60% chance to rise 10%, and 40% chance to decrease 10%. What is the probability of at least X breaking even if X cashes out after 4 years. I don't know how to arrive since can't use normal binomial distribution due to having the "at least part" (3 OR 4 years of positive growth). Tried to go the other way around, since 3 losses means not breaking even but 1-nCr(4,3)*0.4^3 *0.6 does not yield the correct answer.

So the cost to X is 66(10)= 660€. Out of 100 times 60 times it goes up to 660+ 66= 725€ and 40 times it goes down to 660- 66= 594€. That is an average of [60(725)+ 40(594)]/100= 672.60€. Now the problem I have you don't say if the "rise 10%" and "decrease 10%" is each year or what time interval.

2) < Link to "Most Viral Images" at imgur removed >.Honestly I don't have a clue as to how to calculate this.

The variance of what study??

3) In hockey penalties have 30% chance of happening. If in penalties where each team do 3 penalties one goalie keeps a clear sheet but the other doesn't? So clear sheet is 0.7^3 but how to proceed from there (chance of at least 1 goal)? Thought about 0.7^3 *(1-0.7^3) but that's not correct.

Again, "30% of happening" over what time interval? One game? What do you mean by a "clear sheet"? Not getting a penalty? Or not allowing a shot? Is the 30% referring to the goalie only? I thought it was for the whole team.

These are old entrance exam questions and I'm practicing maths portion but its been quite a while since I was in gymnasium and needed these specific calculations so if someone can show me how to calculate these it would help me immensely as to understand the maths behind them.

 

[1211212]

So the cost to X is 66(10)= 660€. Out of 100 times 60 times it goes up to 660+ 66= 725€ and 40 times it goes down to 660- 66= 594€. That is an average of [60(725)+ 40(594)]/100= 672.60€. Now the problem I have you don't say if the "rise 10%" and "decrease 10%" is each year or what time interval.


The variance of what study??


Again, "30% of happening" over what time interval? One game? What do you mean by a "clear sheet"? Not getting a penalty? Or not allowing a shot? Is the 30% referring to the goalie only? I thought it was for the whole team.

My apologies that I haven't been clear enough.

1) its yearly. So 10% de/increase a year. 60% of going up by 10 points, 40% chance of going down 10 points.

2) Study might be the wrong word, but the question is regarding the table there, and that formula tells how to calculate the sample variance. It gives both women and men in the "study" and their respective values and now it asks variance for the whole thing. So if partitioned to men and women you get aforementioned values, what would the variance be if combined. Also the first cells are sample *size*

3) Shooting a penalty and scoring a goal has 30% chance. Keeping a clear sheet means that one goalie blocks all the shots/they miss, so 70% chance of that happening. So the 30% is for the shooter, each, regardless of other factors, of scoring the goal. So the chance of keeping a clear sheet clear sheet is 70% to the power of three.

 

[Deleted member 4993]

2)< Link to "Most Viral Images" at imgur removed >. Honestly I don't have a clue as to how to calculate this.

In probability theory and statistics, variance is the expectation of the squared deviation of a random variable from its mean. Informally, it measures how far a set of (random) numbers are spread out from their average value.
Please google the following key-words: "variance statistics"
You will find helpful videos and papers explaining calculation of variance under different conditions.

 

[1211212]

In probability theory and statistics, variance is the expectation of the squared deviation of a random variable from its mean. Informally, it measures how far a set of (random) numbers are spread out from their average value.
Please google the following key-words: "variance statistics"
You will find helpful videos and papers explaining calculation of variance under different conditions.

Yes I understand the definition, but I cannot find examples like this one. So we have the x, x (variance with the top on), and n from the partial infos. Can I add them together, and will they remain the same? I seem to not be able to google myself the answer, maybe because I don't know the proper terms or its not as common? Due the answer being 5.05 I just can't seem to find a way to get to that conclusion.

E: Do we even have to use other numbers other than the sample variances? The new variance would be 4²+9² but that's way off the answer

 

[Deleted member 4993]

This is more of an algebra problem than statistical one.

Please expand (x_M -m_M)²

Add to it:

(x_W -m_W)²

What do you get?

 

[1211212]

This is more of an algebra problem than statistical one.

Please expand (x_M -m_M)²

Add to it:

(x_W -m_W)²

What do you get?

2x²-4xm+2m²