A Bernoulli random variable is one that assumes only two values, 0 and 1 with p(1) = p and p(0) = 1 − p ≡ q.
a Sketch the corresponding distribution function.
b Show that this distribution function has the properties given in Theorem 4.1.
Step1 of 3:
Let us consider a random variable X it follows bernoulli distribution with parameter ‘p’.
And range from 0 and 1 with P(0) = p and P(1) = 1 - p
Here our goal is:
a). We need to sketch the corresponding distribution function.
b). We need to Show that this distribution function has the properties given in Theorem 4.1.
Step2 of 3:
The distribution of X is given by:
The graph of the corresponding distribution function is:
Step3 of 3:
The distribution function of p is 0 everywhere except 0 and 1 thus:
Therefore F is a non-decreasing function of X: