Discover a world of knowledge at Westonci.ca, where experts and enthusiasts come together to answer your questions. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.

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

Sagot :

fichoh

Answer:

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