Properties of discrete probability distribution

.

1. PROPERTIES OF DISCRETE PROBABILITY DISTRIBUTION MS. MA. JACQUELYN L. MACALINTAL MAED STUDENT ADVANCED STATISTICS

2. PROPERTIES OF DISCRETE PROBABILITY DISTRIBUTION 1. The sum of all probabilities should be 1. 2. Probabilities should be confined between 0 and 1. P (X) = 1 0 ≤ P (X) ≤ 1 Number of Heads, X 1 2 Probability, P(X) 1 _ 4 1 _ 2 1 _ 4 P (X) = 1 _ 4 1 _ 4 1 _ 2 + + = 1  

3. Example 1: Determine whether the distributions is a discrete probability distribution. P (X) = 1 0 ≤ P (X) ≤ 1 X 3 6 8 P(X) -0.3 0.6 0.7 a. X 1 2 3 4 5 P(X) 3 _ 10 1 _ 10 1 _ 10 2 _ 10 3 _ 10 b . No, it is not a discrete probability distribution, P(X) cannot be -0.3 Yes, it is a discrete probability distribution,  

4. H T H T H T H T H T H T H T Example 3: Supposed three coins are tossed. Let Y be the random variable representing the number of tails. Construct the probability distribution and draw the histogram. Sample Space: { HHH, HHT, HTH, HTT, THH, THT, TTH, TTT }

5. Example 2: Supposed three coins are tossed. Let Y be the random variable representing the number of tails. Construct the probability distribution and draw the histogram. Possible outcomes Value of the random variable Y (number of tails) HHH HHT 1 HTH 1 HTT 2 THH 1 THT 2 TTH 2 TTT 3 Number of tails, Y 1 2 3 P(X) 1 _ 8 3 _ 8 3 _ 8 1 _ 8 1 _ 8 2 _ 8 3 _ 8 0 1 2 3

6. - Anonymous