(Dont need an explanation or work shown just the answer)

1. Let X be a random variable that can take on five values: 2, 3, 4, 5 and 6. The probability density function is f(x) = cx² for the possible values of x (i.e. 2,3,4,5 and 6). What value of c ensures that the density function satisfies all properties of well-defined probability density functions?

Group of answer choices

1/400

1/5

1/90

1/20

1/25

2. Using the information obtained in Question 1 (including the calculated value of c), what is the P( X > 4 / X > 2)?

Group of answer choices

.71

.95

.14

.50

.86

3. Using the information obtained in Question 1, what is the variance of the random variable Y defined as Y = 2X?

Group of answer choices

1.37

4.89

23.91

5.46

2.73