Im getting confused between experimental probablity and expected value definition. I see in the notes its mentioned experimental probablity for getting heads is the number of times we record heads for the 20 trials we perform in an experiment. Then how it is different from expected value?
2. Also what is rhe difference between categorical and numerical expected value. I still did not understand how the probability was calculated for a , b and c area in the dart board scenario.
So experimental probability is the probability we assign a given outcome based on empirical data. For example, we throw a coin 10 times and get heads 6 time, so we assume an experimental probability of 6/10 = 0.6 of getting heads on a given throw.
The expected outcome is the average outcome we expect to get after infinitely-many trials. For example, we know the true probability of getting heads is 0.5 on any given throw. Then, in 10 throws, we expect to get, on average 5 heads, so it’s the expected value. The way expected value is computed is we take each possible outcome (0, 1, 2 etc) and multiply it by its probability of occurring before adding up these products. That way if certain outcomes (like 4 or 5) are more likely than others (0 or 10), then we’re adding this to the estimation. It’s like a weighted average where the weight of each outcome is its likelihood to occur.
Also what is the difference between categorical and numerical expected value.
Unless we have only two categories, the expected value for categorical variables doesn’t make much sense, because any numeric values we attribute to each outcome are rather arbitrary because we’re assigning them.
I still did not understand how the probability was calculated for a , b and c area in the dart board scenario.
These were “given”. We just assume we know these are the probabilities for each region based on something like the area of each sector. Because the purpose of this lecture was to explain expected values, we just assumed we know the probabilities of each outcome on the sample space in order to compute the expected value of the event.
Hope these help!