The Basics of Bernoulli Distribution with Probability of Success π=0.3
What is the formula for the distribution of Bernoulli with probability of success π=0.3?
1. What does the function π(π₯) represent in the context of Bernoulli trial?
2. How is the probability of success and failure calculated in the formula?
3. What values can the variable π₯ take in the formula?
Answer:
The distribution of Bernoulli with π=0.3 is represented by the formula π(π₯) = (0.3)^π₯ * (0.7)^(1-π₯).
The function π(π₯) represents the probability of a Bernoulli trial with a success probability of π=0.3. When π₯=0, the formula simplifies to (0.3)^0 * (0.7)^1, which equals 0.7, representing the probability of failure. When π₯=1, the formula simplifies to (0.3)^1 * (0.7)^0, which equals 0.3, representing the probability of success.
The values of 0.3 and 0.7 in the function represent the probabilities of success and failure respectively. The exponent π₯ determines whether the success or failure probability is used in the calculation. For example, if π₯=1, the success probability of 0.3 is used. If π₯=0, the failure probability of 0.7 is used.
In summary, the distribution of Bernoulli with π=0.3 is given by π(π₯) = (0.3)^π₯ * (0.7)^(1-π₯), where π₯ can take on the values 0 or 1.