Question

Jack enjoys the game Cornhole. (FYI: This is a game where you throw bags at a board with a hole in it.)

Let X be the random variable that represents the number of bags that Jack scores with on his turn.

The table below shows the probability distribution for X.

x	0	1	2	3	4
p(x)	?	0.05	0.33	0.48	0.10

(a) What must p(0) = P(X = 0) be?

(b) Calculate the following probabilities: i. P(X = 0 or X = 4) ii. P(X ≥ 3)

(c) Calculate µ, the average or expected value of X.

(d) Calculate σ, the standard deviation of X.

Answer 1

Total sum of all probability must be equal to one.

a) P(X = 0) + 0.05 + 0.33 + 0.48 + 0.1 = 1

or, P(X = 0) = 0.04

b) i) P(X = 0 or X = 4) = P(X = 0) + P(X = 4) = 0.04 + 0.1 = 0.14

ii) P(X > 3) = P(X = 3) + P(X = 4) = 0.48 + 0.1 = 0.58

c) µ = E(X) = 0 * 0.04 + 1 * 0.05 + 2 * 0.33 + 3 * 0.48 + 4 * 0.1 = 2.55

d) E(X²) = 0² * 0.04 + 1² * 0.05 + 2² * 0.33 + 3² * 0.48 + 4² * 0.1 = 7.29

Var(X) = E(X²) - (E(X))² = 7.29 - 2.55² = 0.7875

SD(X) = σ = sqrt(0.7875) = 0.89