Question

1. Provide an example of a discrete probability distribution. Explain how the example meets the criteria for a probability distribution.

2. What would be the expected value of the probability distribution used as an example in the previous question? Report the value and describe what it represents.

Answer 1

Let a coin is tossed once whose probability of getting head to be p and that of tails is 1-p. ( 0<p<1 )

Let X be the number of heads.

X can take only discrete values 0 and 1.

Hence X is a discrete random variable.

p(x) = 1-p if X = 0

and p(x) = p if X = 1

This  example meets the criteria for a probability distribution because:

0 < p(x) < 1 for all x

And $\sum p(x)$ = p + (1-p) = 1

Now,

Expected value = E[X] = = 0*(1-p) + 1*p = p

xp(2)

This value represents the number of heads when this experiment is done a large number of times.

If there were n tosses, the expected value would simply been np. Which is the anticipated number of heads in n tosses.