Random Variables + Probability (U6)

Pretend you added the data points of data set x to dataset y. How would you calculate the new standard deviation?

*you can't just add the standard deviation from each individual plot together! 1) variance of x + variance of y 2) take the square root of the new variance

What formula do you use to find the new standard deviation when subtracting one distribution form another?

*you use the same formula whether you are doing addition or subtraction o(x+y or x-y) = sqrt(ox^2 + oy^2) standard deviation = the square root of (the variance of x + the variance of y) - variance = (standard deviation)^2

What formula should you use to find the new mean when adding one distribution to another?

M(x+y) = M(x) + M(y) Mean of x+y = the mean of x + the mean of y

What formula should you use to find the new mean when subtracting one distribution from another?

M(x-y) = M(x) - M(y) Mean of x-y = the mean of x - the mean of y

Why does the standard deviation of a distribution change when you multiply the data by a constant?

if you were to multiple a dataset by 2 the data would become more spread out, meaning the standard deviation would increase

What is the formula for calculating the standard deviation for binomial distributions?

ox = sqrt(np(1-p) standard deviation = the square root of ((# trials)(probability)(1-probability)

What happens to the shape, center, and standard deviation when you add or subtract a constant (c) from a dataset?

shape: same center: add/subtract c variability: same

What happens to the shape, center, and standard deviation when you multiply or divide a dataset by a constant (c)?

shape: same center: multiply/divide by c variability: multiply/divide by c

What is the formula for calculating the mean for binomial distributions?

ux = np mean = (number of trials)(probability)

How do you calculate variance when you have the value of standard deviation?

variance = (standard deviation)^2

What are the 4 conditions for a binomial setting? *hint: bins

1) Binary: each trial is a success or failure 2) Independent: each trial is not influenced by the others 3) Number: there is a fixed number of trials (n= ) 4) Same probability of success for each trial (p= )

Pretend you added the data points of data set x to dataset y. How would you calculate the new mean?

The new mean would be the mean of plot x + the mean of plot y

Pretend you added the data points of data set x to dataset y. How would you calculate the new variance?

The new variance would be the variance of plot x + the variance of plot y

How do you find the probability of a range on the calculator for a binomial distribution? ex: the chance that a person gets at most 3 correct

do 2nd => vars => binomcdf

How do you find the probability an exact amount on the calculator for a binomial distribution? ex: the chance that a person gets exactly 3 correct

do 2nd => vars => binompdf Pdf = Precise