Evaluate the cumulative distribution function of a binomial random variable with n equals 3 and p equals 1 divided by 6 at specified points. Give exact answers in form of fraction. Upper F left-parenthesis 0 right-parenthesis equals Upper F left-parenthesis 1 right-parenthesis equals Upper F left-parenthesis 2 right-parenthesis equals Upper F left-parenthesis 3 right-parenthesis equals

125/216

25/72

5 / 72

1 / 216

Step-by-step explanation:

n = 3

p = 1/6 = 0.1667

Using the relation :

P(x =x) = nCx * p^x * (1 - p)^(n - x)

F(0) = 3C0 * (1/6)^0 * (1 - 1/6)^3

F(0) = 1 * 1 * (5/6)^3

F(0) = 1 * 125/216

F(0) = 125 / 216

F(1) = 3C1 * (1/6)^1 * (1 - 1/6)^2

F(1) = 3 * 1/6 * (5/6)^2

F(1) = 3 * 1 / 6 * 25/36

F(1) = 75 / 216

F(1) = 25 / 72

F(2) = 3C2 * (1/6)^2 * (1 - 1/6)^1

F(2) = 3 * 1 / 36 * (5/6)^1

F(2) = 3 * 1/36 * 5/6

F(2) = 15/216

F(2) = 5/72

F(3) = 3C3 * (1/6)^3 * (1 - 1/6)^0

F(3) = 1 * 1 /216 * (5/6)^0

F(3) = 1 * 1/216

F(3) = 1/216