Question

A cube has its six sides colored red, white, blue, green, yellow, and violet. It is assumed that these six sides are equally likely to show when the cube is tossed. The cube is tossed once. (a) Describe the sample space. (b) Consider the random variable that assigns the number 0 to red and white, the number 1 to green and blue, and the number 2 to yellow and violet. What is the distribution of this random variable? (c) Let Y = (X + 1)^2, where X is the random variable in part (b). Find E(Y).

Answer 1

Answer:

(a) S= {red, white, blue, green, yellow, violet}

(b) $P(X=0) = \frac{1}{3}; \ \ P(X=1) = \frac{1}{3};\ \ P(X=2) = \frac{1}{3};$

(c) E(Y) = 4.67

Step-by-step explanation:

(a) The sample space 'S' is:

S= {red, white, blue, green, yellow, violet}

(b) Since all three values are assigned to two different colors, there is a 2 in 6 chance that each value will be assigned, the distribution of this random variable is:

$P(X=0) = \frac{1}{3}; \ \ P(X=1) = \frac{1}{3};\ \ P(X=2) = \frac{1}{3};$

(c) The expected value of Y is:

$E(Y) = \frac{1}{3}*[(0+1)^2]+ \frac{1}{3}*[(1+1)^2]+\frac{1}{3}*[(2+1)^2]\\E(Y) = 4.67$