If 0 and 1 are the only possible values of the random variable x, and if P(0) = 0.3 and P(1) = 0.7, what would be the mean of this probability distribution?

Question

I'm having trouble solving this.

Answer 1

The "mean" is another way to say the "expected value." That is, what value do we expect to get? The mean doesn't have to be any of the values that can actually occur, it just gives you an idea of what you can expect the value to be around.

 

For your distribution, you can probably guess that the expected value is between 0 and 1, but slightly closer to 1 than to 0 (since it's more likely that 1 will occur than that 0 will occur). Here's how you actually calculate the mean:

 

(value one) × (probability of value one) + (value two) × (probability of value two) + ... + (last value) × (probability of last value)

 

For your distribution, that's:

 

0 × P(0) + 1 × P(1) = 0 × 0.3 + 1 × 0.7 = 0 + 0.7 = 0.7