Final answer:
The question involves comparing empirical data with theoretical probability using a deck of cards as an example. The theoretical probability of selecting a diamond is 1/4, and experiments both with cards and simulation aim to determine the binomial distribution of this probability.
Step-by-step explanation:
The student's task involves understanding the concept of empirical data and comparing it with theoretical probability using a deck of cards as an example of a discrete distribution. A standard deck of cards has 52 cards divided into four suits: spades, hearts, diamonds, and clubs, each with 13 cards. The theoretical probability of picking a diamond from a well-shuffled deck is 13 out of 52, or 1/4 since there are 13 diamonds in a deck. The procedure for this experiment is to shuffle the deck, pick a card, and record whether it is a diamond or not. After recording, the card is put back, the deck is reshuffled, and the process is repeated.
The variable X represents the number of diamonds picked out of 10 tries, and theoretically, it follows a binomial distribution with parameters n=10 (number of trials) and p=1/4 (probability of success on each trial). When organizing the empirical data, one would count the number of diamonds actually picked from the shuffled deck and calculate the relative frequency, which is the number of successes (diamonds picked) divided by the total number of trials (card picks).
For simulating the same procedure with a calculator and randInt function, random integers representing card suits can be generated. The number of times '3' (representing diamonds) appears in the simulation of 10 draws would be the empirical value of X in the simulated data. This data can also be organized and compared with theoretical expectations using relative frequency.