The probability distribution of a discrete random variable x is given by: p(x = −1) = 1 5 ,p(x = 0) = 2 5 and p(x = 1) = 2 5 (a) compute e[x]. (b) determine the probability distribution y = x 2 and use it to compute e[y ]. (c) determine e £ x 2 ¤ using the change-of-variable formula. (you should match your answer in part (b). (d) determine v ar (x).

Step-by-step explanation:

Given that the probability distribution of a discrete random variable X is given by:

a)

b)

So y can take values as 0 and 1.

P(Y=0) =

P(Y=1) =

(since -1 also becomes +1 when squared)

E(Y) =

c)

d) Var(x) =

first option

a function is a relation in which an input is paired with exactly one output.

so, let's find the right answer.

in our first option, our inputs are january, february, and march. the outputs are 30, 28, and 25. each input has it's own output. this is correct!

our second option we know is incorrect, because ms. valverade has two outputs, dogs and cats. this is not a function.

our third option is incorrect as well. the yellow square has two ouputs, the square and the triangle.

lastly, in our fourth option, we see the number 7 two times with a different output. therefore, this is not a function.

remember: each input must be paired with only one output!