Stats exam 2

Flip a coin 3 times to see if its heads or tails

2³ = 8 outcomes

random variable

a variabel whose posssible outcomes are numeric values and whose probabilities are assigned according to some fucntion or rule

discrete random variable

a random variabel that can take on a countable number of outcomes

continuous random variable

a random variable that can take on any numeric value

time spent waiting for a customer to checkout in a gorcery store

continuous vairable [0,30]

time can be broken up into tiny incriments infinite

what is the probability of winning <1000 on a single planko chip

p(x=500, x=100, x=0) add up all of their probs

disjoint events because you cant win two events at once

given that money was won what is the probabilty that the chip landed on 100000

P(x=100000 / x>0) = P(x=100k and x>0/P(x>0))

bayes rule

P(A∣B)=P(B)P(B∣A)P(A)​

if 2 chips are dropped what is the prob that they willl land in the 1000 slot

x1= result of first chip x2= result of 2nd chip

use multiplication rule for independent events P(x1=1000 and x2=1000) = 0.242 × 0.242 = 0.059

random variable

a variable whose outcomes are numeric values and whose probabilties are assigned according to some function or rule

expected value

the average outcome from a probability model if the ranodm expeirment is repeated ad infinitum

E(x) = x1P(x=x1) + … + xkP(x=2)

E(x+/-c)

where c is constant

E(aX) =

aE(x)

E(x+y) or E(x=y)

E(x) + E(y) or E(x) - E(y)

SD(X±c)

Where c is constant

SD(aX)

abolsute value of a

SD(x+y)

Sqrt of (sd(x)² + sd(y)²) same thing for minus

binomial model

discrete probability distribution that calculates the probability of observing k number of siuccesses in n fixed number of independent trials

n is the number of trials

k is the number of successes