Find the expected value of the number of questions you'd get right by guessing. What are the variance and standard deviation?

- hockeychick23

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- hockeychick23

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- hockeychick23

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- hockeychick23

@jim_thompson5910 can you help me please?

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## More answers

- jim_thompson5910

X = number of correct questions
|dw:1433396801483:dw|

- jim_thompson5910

multiply X and P(X) to form the X*P(X) column of values

- hockeychick23

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- jim_thompson5910

good

- jim_thompson5910

now add up the values in the X*P(X) column and you will get the expected value

- hockeychick23

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- jim_thompson5910

so the expected value is 0.5
which means, you expect (on average) to get 0.5 questions right if you randomly guessed

- hockeychick23

ohhh ok thanks!

- jim_thompson5910

now onto the second part "What are the variance and standard deviation? "

- jim_thompson5910

you're going to have 2 additional columns. I'm going to erase the X*P(X) column to make room

- jim_thompson5910

instead I'm going to have X - mu and (X - mu)^2
|dw:1433397803766:dw|

- jim_thompson5910

mu = expected value = 0.5

- jim_thompson5910

oh wait, there's one more column needed
the P(X)*(X-mu)^2 column
|dw:1433397806736:dw|

- hockeychick23

oh ok, so do i find the mean of p(x)?

- jim_thompson5910

you're asking about the value of mu?
mu = 0.5 and it was found when you computed the expected value

- hockeychick23

oh ok sorry it took me a while to calculate the numbers

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- jim_thompson5910

this is what I'm getting

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- jim_thompson5910

I see the typo you made. Look at the bottom row, last column

- jim_thompson5910

you should have (2-0.5) and not (1-0.5)

- hockeychick23

sorry i pasted the wrong table this is what i got

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- hockeychick23

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- jim_thompson5910

btw if you have excel or open office (it should work in there too), you can type in formulas like you see attached

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- jim_thompson5910

that way you can automate things a bit

- hockeychick23

Ok thanks

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- jim_thompson5910

now add up everything in the P(X)*(X-mu)^2 column, you should get 0.375

- jim_thompson5910

0.375 is the variance
take the square root of the variance to get the standard deviation

- hockeychick23

standard deviation= .61237243569
variance= 0.375

- jim_thompson5910

looks good

- hockeychick23

ok thanks so much! i have a question pertaining to the same data that i need help with if you can help me with it:
Let's say that for one of the two questions you can narrow the answer choices down to three. Now your chance of getting that question right by guessing is about .33. What is the new expected value for the number of questions you'd get right by guessing? What are the new variance and standard deviation of this random variable? Drawing another tree diagram and making another probability distribution table may help you answer this question.
I'll give you another medal

- jim_thompson5910

were you able to get started on this one? or no?

- hockeychick23

sort of but I'm not sure if i did it right, i did

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- jim_thompson5910

I made question 1 have P(correct) = 0.33
and question 2 has P(correct) = 0.25
|dw:1433401116557:dw|

- jim_thompson5910

are you seeing how I'm getting these values?

- hockeychick23

ohhh yes thanks!

- jim_thompson5910

so here is getting 0 questions correct
|dw:1433401932751:dw|
ie getting both wrong

- jim_thompson5910

0.0825 is cut off, but that's getting both correct
|dw:1433401967587:dw|

- hockeychick23

Ok so 0.5025 is the probability of getting 0 correct and 0.0825 is getting both correct.

- jim_thompson5910

and the other values are added to get the probability of getting exactly 1 correct
so that gives us this new table
|dw:1433402014075:dw|

- jim_thompson5910

yes

- hockeychick23

Ok so would i need to find the expected value again?

- hockeychick23

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- jim_thompson5910

this is what I get

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- jim_thompson5910

You have 0.825 instead of 0.0825

- jim_thompson5910

So I'm getting an expected value of 0.58
and a variance of 0.4086
standard deviation = sqrt(variance) = sqrt(0.4086) = 0.63921827 (approximate)

- hockeychick23

ok now I'm getting that too, thanks! (I'm going to post something and tag you in it to give you another medal)

- jim_thompson5910

that's fine, it doesn't matter about the medal thing lol

- jim_thompson5910

I'm glad it's making sense now

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