Question

1. What is a probability distribution? Provide an example and discuss its basic features.
2. What do we mean when we say two events are independent? please Explain

Answer 1

Answer 1)

Probability distribution is the function that provides probability of all the possible outcomes of the experiment performed.

Its features are

1) sum of all the probabilities is always equal to 1

2) Each and every probability is in between 0 and 1

Example

Lets say we are tossing a coin and want the probability distribution of all the possible outcomes

First out come can be heads

Probability of getting heads = 0.5 (as we have two possible out comes either heads or tails, p(heads) = 1/2 = 0.5}

Similarly P(tails) = 1/2 = 0.5

We can see that all the probabilities are between 0 and 1

And sum is also equal to 1 (0.5+0.5 = 1)

2)

When two events are independent then it means probability of occurence of one event doesn't have effect on the probability of other.

For example probability of getting heads in the next toss will always be 0.5, it doesn't matter if we had heads or tails in the previous toss.