x: 0, 1, 2, 3, 4; P(x): 0.1, 0.2, 0.4, ?, 0.1, find the missing…

Step by step, with the reason for every step · Random variables · University Statistics

Step by step

Question: x can be 0, 1, 2, 3, 4, with probabilities 0.1, 0.2, 0.4, a missing one, 0.1: find the missing probability.

x: 0, 1, 2, 3, 4; P(x): 0.1, 0.2, 0.4, ?, 0.1

x always takes one of its values.

So all the probabilities add up to 1.

a probability table always adds up to 1

0.1 plus 0.2 plus 0.4 plus P of 3 plus 0.1 is 1.

0.1 + 0.2 + 0.4 + P(3) + 0.1 = 1

The known ones add up to 0.8.

0.8 + P(3) = 1

To remove the plus 0.8, we take away 0.8 on both sides.

1 minus 0.8 is 0.2.

P(3) = 1 − 0.8 = 0.2

Careful!

The missing probability is what is left over from 1.

Careful: the missing P is what is left of 1

Let's check: 0.1 plus 0.2 plus 0.4 plus 0.2 plus 0.1 is 1.

So it is right!

0.1 + 0.2 + 0.4 + 0.2 + 0.1 = 1

Let's look back.

First: all P(x) add to 1.

Last: check.

Answer

Careful: the missing P is what is left of 1

Try this one yourself, then check:

X can be 0, 1, 2, 3, 4, with probabilities 0.1, 0.3, 0.2, a missing one, 0.2: find the x: 0, 1, 2, 3, 4; P(x): 0.1, 0.3, 0.2, ?, 0.2

Show the answer

P(3) = 0.2