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

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

Mathematics
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@jim_thompson5910 can you help me please?

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X = number of correct questions |dw:1433396801483:dw|
multiply X and P(X) to form the X*P(X) column of values
good
now add up the values in the X*P(X) column and you will get the expected value
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so the expected value is 0.5 which means, you expect (on average) to get 0.5 questions right if you randomly guessed
ohhh ok thanks!
now onto the second part "What are the variance and standard deviation? "
you're going to have 2 additional columns. I'm going to erase the X*P(X) column to make room
instead I'm going to have X - mu and (X - mu)^2 |dw:1433397803766:dw|
mu = expected value = 0.5
oh wait, there's one more column needed the P(X)*(X-mu)^2 column |dw:1433397806736:dw|
oh ok, so do i find the mean of p(x)?
you're asking about the value of mu? mu = 0.5 and it was found when you computed the expected value
oh ok sorry it took me a while to calculate the numbers
this is what I'm getting
I see the typo you made. Look at the bottom row, last column
you should have (2-0.5) and not (1-0.5)
sorry i pasted the wrong table this is what i got
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btw if you have excel or open office (it should work in there too), you can type in formulas like you see attached
that way you can automate things a bit
Ok thanks
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now add up everything in the P(X)*(X-mu)^2 column, you should get 0.375
0.375 is the variance take the square root of the variance to get the standard deviation
standard deviation= .61237243569 variance= 0.375
looks good
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
were you able to get started on this one? or no?
sort of but I'm not sure if i did it right, i did
I made question 1 have P(correct) = 0.33 and question 2 has P(correct) = 0.25 |dw:1433401116557:dw|
are you seeing how I'm getting these values?
ohhh yes thanks!
so here is getting 0 questions correct |dw:1433401932751:dw| ie getting both wrong
0.0825 is cut off, but that's getting both correct |dw:1433401967587:dw|
Ok so 0.5025 is the probability of getting 0 correct and 0.0825 is getting both correct.
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|
yes
Ok so would i need to find the expected value again?
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this is what I get
You have 0.825 instead of 0.0825
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)
ok now I'm getting that too, thanks! (I'm going to post something and tag you in it to give you another medal)
that's fine, it doesn't matter about the medal thing lol
I'm glad it's making sense now

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