Question

The probability distribution function for the discrete random variable where x is equal to the number of red lights drivers typically run in a year is as follows. x 0 1 2 3 p(x) 0.76 0.15 0.05 (a) Fill in the missing probability. x 0 1 2 3 p(x) 0.76 0.15 0.05 (b) What is the mean of this discrete random variable

Answer 1

Using probability concepts, it is found that:

a) The missing value is 0.04.

b) The mean is of 0.37.

The distribution is given by:

$P(X = 0) = 0.76$

$P(X = 1) = 0.15$

$P(X = 2) = 0.05$

$P(X = 3) = x$

Item a:

The sum of all the probabilities has to be 1, that is:

$\sum_{i = 0}^{3} P(X = i) = 1$

Thus:

$0.76 + 0.15 + 0.05 + x = 1$

$0.96 + x = 1$

$x = 0.04$

The missing value is 0.04.

Item b:

The mean is given by the sum of each outcome multiplied by it's probability, thus:

$E(X) = 0(0.76) + 1(0.15) + 2(0.05) + 3(0.04) = 0.37$

The mean is of 0.37.

A similar problem is given at https://brainly.com/question/20709747