The binomial distribution is defined for events with two probability outcomes and for events with a multiple number of times of such events. The Poisson distribution is based on the numerous probability outcomes
The example in the Mplus manual has an example for three categories. Is this correct? P(Y=1|x)=F(t1 - b1*x1+b2*x2...) P(Y=2|x)=F(t2 - b1*x1+b2*x2...) - F(t1-b1*x1+b2*x2...) P(Y=3|x)=F(t3 - b1*x1+b2*x2...) - F(t2 - b1*x1+b2*x2...) ...
If you have two mutually exclusive events, the probability of getting A and B is actually 0—so P(A ∩ B) = 0. Let’s revisit our black-or-red example. In this bet, getting a red pocket on the roulette wheel and getting a black pocket are mutually exclusive events, as a pocket ...
So, if two events are independent, each event’s probability remains the same, regardless of the other event’s occurrence. For example, Barcelona becoming champion in Spain is (mostly) independent of Juventus becoming champion in Italy. These two ways of expressing their independence are equivalen...
conditionalprobabilityindependenteventsThe article offers insights for mathematics enthusiasts on how to calculate dependent probabilities, in which bookkeepers were offering odds of 4:1 on France team winning the 2004 European soccer competition and the odds of 8:1 on Thierry Henry being the top ...
Bonus Example Problem! Our ultimate goal as a random packer is that we’d like to have two tan pants and two blue shirts in our suitcase. Can you figure out how to calculate that probability given the above information? To solve that problem, we’ll define two tan pants as event 2TP ...
For example, if the hypothesized contributor is homozygous for the A allele, we compute the conditional probability of sampling an additional copy of the A allele given that the suspect has the AA genotype P(A|AA). This essentially uses the Balding-Nichols sampling formula [15], but for ...
Tip:We can also consider the relative frequencies from the body of the table, referred to as a conditional relative frequency. For example, what would be the relative frequency of people from Street A who did not see a patrol? We know that 40 people were from Street A, and in looking ...
For example, the probability that slope is likely in [0°, 1°] is 52%, and that it must be in [0°, 1°] is 26%, forming a belief interval of [26%, 52%] with an uncertainty of 26%. Similarly, the probability that slope is likely in [1°, 2°] is 67% (93%−26%),...
Key Elements of Value at Risk Specified amount of loss in value or percentage Time period over which the risk is assessed Confidence interval Example VaR Assessment Question If we have a 95% confidence interval, what is the maximum loss that can occur from this investment over a period of one...