Question

1. Consider a continuous random variable X with a probability density function that is normal with mean 0 and standard deviation What is the probability that X = 0? Explain your answer.

2. Is each outcome of the roll of a fair die an independent Bernoulli trial? Why or why not?

Answer 1

1)

For any continuous distribution, probability of random variable X equal to any particular value is zero.

For example in Normal distribution, P(X=0) = 0

As probability of (X<0) is area under curve between 0 and - infinity.

2) Yes

In bernoulli distribution we have two outcomes 'success' and 'failure'.

In an experiment of rolling a fair die, it is independent Bernoulli trial. Out of six outcomes, for example when 1 occurs then it's a 'success' and otherwise it's a 'failure' for remaining 5 outcomes.