Question

For a discrete random variable that takes a value of 8 with probability .75 and a value of -4 with probability of .25, what is the expected value and what is the variance

Answer 1

5.20

Explanation:

X : ______ 8 ____ - 4

P(X) : ___ 0.75 __ 0.25

The expected mean E(x) :

E(x) = ΣX / n

n = sample size = 2

E(x) = (8*0.75) + (-4*0.25)

E(x) = 6 - 1

E(x) = 5

The standard deviation : sqrt(Var(x))

Var(x) = Σx²p(x) - E(x)²

Var(x) = (8^2 * 0.75) + (-4^2 * 0.25)) - 5^2

Var(x) = ((64 * 0.75) + (16* 0.25)) - 25

Var(x) = (48 + 4) - 25

Var(X) = 27

Standard deviation = sqrt(27)

Standard deviation (x) = 5.1961524

Standard deviation = 5.20