Sidney Crosby’s score statistics for the regular 2007 championship season were used to construct the following table:
Experimental Outcome (x), Number of Occurrences during the 2007 Season
(0, 358) (1, 175) (2 28) (3 3) (4 10)
a. Use the relative frequency method to create an empirical discrete distribution. Assign probabilities to each outcome
b) b. Calculate the E(x). [Note: For your calculation, use values of f(x) rounded to three decimal places.]
See first name lolllllll hint hint
a) To create an empirical discrete distribution using the relative frequency method, we need to calculate the probabilities of each outcome by dividing the number of occurrences by the total number of occurrences. The total number of occurrences in this case is the sum of all the numbers of occurrences:
Total number of occurrences = 358 + 175 + 28 + 3 + 10 = 574
Using this total, we can calculate the probabilities:
P(X = 0) = 358 / 574 = 0.623
P(X = 1) = 175 / 574 = 0.305
P(X = 2) = 28 / 574 = 0.049
P(X = 3) = 3 / 574 ≈ 0.005
P(X = 4) = 10 / 574 = 0.017
Therefore, the empirical discrete distribution with assigned probabilities is:
X | P(X)
-------------
0 | 0.623
1 | 0.305
2 | 0.049
3 | ~0.005
4 | 0.017
b) To calculate E(x), we need to multiply each outcome by its corresponding probability, and then sum up the results:
E(x) = 0 * 0.623 + 1 * 0.305 + 2 * 0.049 + 3 * ~0.005 + 4 * 0.017
Calculating this expression gives us the expected value:
E(x) = 0 + 0.305 + 0.098 + ~0.015 + 0.068 = 0.456
Therefore, the value of E(x) for this empirical discrete distribution is approximately 0.456.