(By the way i have directly jumped to LOS 10 without doing anything much in the earlier LOS's because CTD suggested that probablility is easier....so CTD the onus is on u!)
Q. Pg. 200 Scwesr Book 1 :
Tell me whats the difference between "Continuous uniform distribution" and "probability density function" explained on pg. 196?
i dont have the schweser`s book with me right now, but i`ll just try to recall what i can remember from my college days. So, i was in the second year and there was this really sweet girl in my microprocessor design class....ooops
Bad jokes apart, continuous uniform distribution has three aspects to it. it is:
1. continuous: meaning, the independant variable can take any value within an interval. For example, when i roll a dice, i can only get values 1,2,3...6. i cant get 5.5, 4.75, etc. When i toss a coin, i can only get head or tail. This is a discrete distribution, since only discrete values can be assumed. in contrast, in a continous distribution, any intermediate value can be assumed. For example, if i drive a car for 100 km and keep varying the speed, any speed on the speedometer can be possible, 60kmph, 61.376 kmph, anything. Now this will be a continuous distribution.
2. uniform: a uniform distribution is one where if i plot the x values (independent values) along the x axis, and the probability values along the y axis, i will get a constant probability graph. Meaning, for any given value of x, the probability will remain constant. in case of the dice, if i plot the possible outcomes (1,2,3,...6) along the x axis, then i get a uniform discreet distribution since the probability of any given value of x is constant (1/6). Im really not able to think of an example in the continuous case, but you get the picture, dont you?
3. distribution: a function and a distribution are two different things. A function can be considered as a mathematical representation of a distribution. if i say f(x)=y, then this is a function. The graph of this function can be thought of as analogous to a distribution. A distribution is expressed by a function. A funtion that expresses the probability distribution mathematically is called a probability distribution function. For example, in the dice rolling example, the probablity density function will be:
f(x) = 1/6, for 10, otherwise.
and the discreet uniform distribution will be a graph with a horizontal line at y = 1/6.
This was fun! Hope i havnt made any gaping mistakes...please correct me if i have.