The Basics of Bernoulli Distribution with Probability of Success 𝑝=0.3

What is the formula for the distribution of Bernoulli with probability of success 𝑝=0.3?

1. What does the function 𝑓(𝑥) 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 𝑥 take in the formula?

Answer:

The distribution of Bernoulli with 𝑝=0.3 is represented by the formula 𝑓(𝑥) = (0.3)^𝑥 * (0.7)^(1-𝑥).

The function 𝑓(𝑥) represents the probability of a Bernoulli trial with a success probability of 𝑝=0.3. When 𝑥=0, the formula simplifies to (0.3)^0 * (0.7)^1, which equals 0.7, representing the probability of failure. When 𝑥=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 𝑥 determines whether the success or failure probability is used in the calculation. For example, if 𝑥=1, the success probability of 0.3 is used. If 𝑥=0, the failure probability of 0.7 is used.

In summary, the distribution of Bernoulli with 𝑝=0.3 is given by 𝑓(𝑥) = (0.3)^𝑥 * (0.7)^(1-𝑥), where 𝑥 can take on the values 0 or 1.